Encoding method, apparatus, computer device and readable storage medium

Abstract

The application relates to the field of finite fields and coding technology, and discloses a coding method, a coding device, computer equipment and a readable storage medium, wherein the method comprises the following steps: acquiring communication data and coding parameters, wherein the coding parameters comprise a square matrix order; a symmetric bilinear form set corresponding to the square matrix order is constructed, each element in the symmetric bilinear form set comprises a first term, a second term and a third term, the coefficients of the first term and the third term are located in a first finite field, the coefficients of the second term are located in a second finite field, the first finite field is a subfield of a base field, the second finite field is an n-th extension field of the base field, the first term is an exponential term with the number of elements of the base field as a base number and with n as an index, n is the square matrix order, and the number of elements of the base field is a prime power; a target code is generated according to the elements in the symmetric bilinear form set, and the communication data is coded by using the target code. The application can improve the diversity of code structures.

Description

Technical Field

[0001] This application relates to the field of finite field and coding technology, and in particular to a coding method, apparatus, computer device and readable storage medium. Background Technology

[0002] Rank-metric codes are codes in a matrix space over a finite field that use rank as the distance metric. Compared to traditional Hamming distance codes, rank-metric codes have significant advantages in scenarios such as resistance to rank-deficit attacks, network coding, and cloud storage error correction.

[0003] Maximum linear symmetric rank distance codes (MRDs) are linear symmetric rank distance codes whose codeword count reaches the theoretical bound, representing the optimal structure within the family of LSDs. Currently, the only known construction method for MRDs is the Schmidt construction. Codewords obtained using the Schmidt construction all begin with... As the primary term, and with the associated linearized polynomial containing a first-order term, the codeword structure is relatively simple and cannot meet the actual needs. Summary of the Invention

[0004] This application provides an encoding method, apparatus, computer device, and readable storage medium that can improve the diversity of codeword structures.

[0005] To achieve the above objectives, the main technical solutions adopted in this application include: In a first aspect, embodiments of this application provide an encoding method, the method comprising: Acquire communication data and encoding parameters, wherein the codeword used for encoding is a symmetric square matrix of even order, and the encoding parameters include the order of the square matrix; Construct a symmetric bilinear set corresponding to the order of the square matrix. Each element in the symmetric bilinear set includes a first term, a second term, and a third term. The coefficients of the first term and the third term are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is an nth-order extension of the base field, and the exponent of the first term uses the number of elements in the base field as its base. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power. Based on the elements in the symmetric bilinear set, a target code is generated, and the target code is used to encode the communication data.

[0006] Secondly, embodiments of this application provide an encoding device, the device comprising: The data acquisition module is used to acquire communication data and encoding parameters, wherein the codeword used for encoding is a symmetric square matrix of even order, and the encoding parameters include the order of the square matrix; A set construction module is used to construct a symmetric bilinear set corresponding to the order of the square matrix. Each element in the symmetric bilinear set includes a first term, a second term, and a third term. The coefficients of the first term and the third term are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is an nth-order extension of the base field, and the exponent of the first term uses the number of elements in the base field as its base. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power. The encoding module is used to generate a target code based on the elements in the symmetric bilinear set, and to encode the communication data using the target code.

[0007] Thirdly, embodiments of this application provide a computer device, including: A memory and a processor, which are communicatively connected to each other, wherein the memory stores computer instructions, and the processor executes the computer instructions to perform the encoding method described in any of the preceding claims.

[0008] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer instructions that cause a computer to perform the encoding method described in any of the preceding claims.

[0009] In some embodiments of the technical solutions in this application, firstly, the exponent term of the first term uses the number of elements in the base field as the base, and... As an exponent, it differs fundamentally from Schmidt's construction, making the maximal linear symmetric rank distance code constructed in this application inequivalent to the maximal linear symmetric rank distance code constructed by Schmidt. Secondly, this application includes the first, second, and third terms, providing space for different code structures and avoiding the problem of degenerating into a single two terms in Schmidt's construction, thus ensuring the diversity of code structures. Finally, the coefficients of the first and third terms lie in the first finite field, the coefficient of the second term lies in the second finite field, and the first finite field is the base field. The nth extension of the base field, with the second finite field as the base field, allows the coefficients of different terms to have different algebraic properties, thereby increasing the diversity of code structures. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0011] Figure 1 A flowchart illustrating the encoding method provided for some embodiments of this application; Figure 2 Encoding and decoding schematic diagrams provided for some embodiments of this application; Figure 3 Schematic diagrams of an encoding apparatus provided for some embodiments of this application; Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0013] Before describing the technical solution of this application, the relevant concepts will be explained first.

[0014] Based on a set of vectors of the same dimension in the matrix , ... Build When only all coefficients are available... , ... Only by taking 0 can the condition be satisfied. =0, then, the vector is called a vector. , ... Linearly independent. Among them, the above... A vector formed by the elements of one row or one column of a matrix. For example, Let the vector consist of the elements of the first row. The vector formed by the elements of the second row. A maximal linearly independent set refers to the set of vectors selected from the row or column vectors of a matrix that has the maximum number of vectors and are linearly independent of each other.

[0015] The rank of a matrix refers to the number of vectors contained in the maximal linearly independent set of row (or column) vectors in the matrix, usually called rank(A).

[0016] Hamming distance code is a code that uses vectors as codewords. In Hamming distance code, corresponding elements in two codewords are compared, and the number of different elements is used as the Hamming distance. For example, if codewords A and B (i.e., vectors A and B) have different 1st, 5th, and 8th elements, then the Hamming distance is 3.

[0017] Rank-distance codes are codes that use matrices over a finite field as codewords. The finite field matrix is ​​a matrix constructed from the elements of that finite field, also known as the base field. In rank-distance codes, the difference between two codewords is the difference matrix, and the rank of this difference matrix is ​​used as the rank distance between the two codewords. For example, subtracting codewords A and B (i.e., matrices A and B) yields a difference matrix C; the rank of difference matrix C is the rank distance between codewords A and B. Compared to traditional Hamming distance codes, rank-distance codes offer significant advantages in scenarios such as resistance to rank-deficit attacks, network coding, and cloud storage error correction.

[0018] In rank-distance codes, if the rank distance between any two different codewords is greater than or equal to d, then the rank-distance code is called a d-code with minimum rank distance d.

[0019] Furthermore, in rank-distance codes, if the addition of any two codewords results in a rank-distance code, then the rank-distance code is called an additive code. In addition to satisfying the additive code requirement, if a rank-distance code is also closed under scalar multiplication over a finite field, then it is called a linear rank-distance code.

[0020] Furthermore, under the same set of parameters (n, q, d), if the number of codewords in a rank-distance code reaches its theoretical bound, then the codeword set is called a maximum-rank-distance code or a maximal-rank-distance code. In the above parameter set, n represents the order of the codewords in the rank-distance code (i.e., the matrix order), for example, an n*n codeword has an order of n. q represents the number of elements in the finite field used to construct the codewords. d is the minimum rank distance of the rank-distance code.

[0021] Furthermore, in rank-distance codes, if every element in a codeword satisfies... , indicating that the codeword is a symmetric matrix, in which case the rank-distance code can be called a symmetric rank-distance code.

[0022] In summary, a maximal linear symmetric rank distance code is a rank distance code that simultaneously satisfies the characteristics of a linear rank distance code, a maximal rank distance code, and a symmetric rank distance code.

[0023] Furthermore, every n*n symmetric matrix has a corresponding symmetric bilinear form T(x,y), where x and y are vectors. T(x,y) is considered a symmetric bilinear form if the following two conditions are satisfied.

[0024] 1) T(x,y) remains linear with respect to both variables x and y. Simply put, it means that if one of the vectors x or y is fixed, T(x,y) is linear with respect to the other vector. For example, if y is fixed, then... And, with x fixed, there exists If so, then T(x,y) is considered to be linear with respect to the two variables x and y respectively.

[0025] 2) T(x,y) satisfies symmetry, that is, T(x,y) = T(y,x).

[0026] There can be a one-to-one correspondence between an n*n symmetric matrix and a symmetric bilinear form T(x,y). Based on one of the symmetric bilinear forms T(x,y), a unique n*n symmetric matrix can be derived. Based on this principle, a set of symmetric bilinear forms can be used to represent a maximal linear symmetric rank distance code. That is, the set of symmetric bilinear forms can include multiple different symmetric bilinear forms T(x,y), each corresponding to an n*n symmetric matrix. Based on one of the symmetric bilinear forms T(x,y) in the set, one of the n*n symmetric matrices in the maximal linear symmetric rank distance code can be derived.

[0027] Based on the above description, this application first provides a symmetric bilinear set as shown in expression (1), which can be used to represent maximal linear symmetric rank distance codes.

[0028] In expression (1), n ​​represents the order of each symmetric matrix (i.e., codeword) in the maximal linear symmetric rank distance code. n can be an even number greater than 4. k takes the value of... .

[0029] q represents the number of elements in the base field. The base field is a symmetric bilinear set. The underlying dataset, and subsequent coefficient determination, field expansion, and operations, are all based on the base field. The number of elements in the base field (i.e., the value of q) is a power of an odd prime number. A prime number is an integer greater than 1 that is only divisible by 1 and itself, such as 2, 3, 5, 7, etc. An odd prime number is a prime number that is odd in value, such as 3, 5, 7, etc. A power of an odd prime number is a number with an odd prime number p as the base and a positive integer t as the exponent, i.e. For example, when p=3 and t=2, .

[0030] Represents the base domain k (i.e. Secondary expansion, This represents the 2k (i.e., n)th order extension of the base field. An extension field is a finite field that is larger than the base field and includes it. The number of elements in is One, expanded domain The number of elements in is For example, when q=9 and k=3, the extended field... The number of elements is One, expanded domain The number of elements in is One. In the following description of this application, Called the first finite field, It is called the second finite field.

[0031] s and n are coprime. Coprime means that s and n are relatively prime, that is, their greatest common divisor is 1. The values ​​of s satisfy... and gcd() represents the greatest common divisor.

[0032] Let be a non-square element located in the second finite field and be a non-square element of the second finite field. Where, for any element 'a' in the second finite field, there exists an element 'm' within the second finite field such that ... If a = 1, then a is a square element of the second finite field; otherwise, a is a non-square element of the second finite field.

[0033] d is the minimum rank distance of the maximal linear symmetric rank distance code.

[0034] Called the first item, Called the second item, It is called the third item. The coefficient of the first term ~ Collectively referred to as the coefficient of the second term, This is called the coefficient of the third term. The coefficients of the first and third terms... , The coefficient of the second term located in the first finite field ~ It is located in the second finite field. The exponent term is called the first term. The exponential term, also known as the second term, The exponential term is called the third term. This is the symmetric term of the second term. The number of symmetric terms in the second term varies depending on the values ​​of n, d, and s. It is the symmetrical term to the third term.

[0035] Tr is the trace function that maps the elements of the extended field back to the base field.

[0036] Based on the above description, the rank-distance code constructed in this application has at least the following properties: 1) The number of codewords can reach the theoretical maximum value.

[0037] Specifically, due to ,therefore For d=4 and nd=n-4 being even, the maximum size is exactly the theoretical maximum value. Therefore, the rank-distance code of this application can reach the theoretical maximum value, which is a maximum code.

[0038] 2) To achieve the minimum rank distance, it is necessary to prove that the rank of the matrix corresponding to any non-zero codeword is at least d. Equivalently, let the self-adjoint linearized polynomial (i.e., q-polynomial) corresponding to the codeword be as shown in expression (2): Then proof is required. Where ker represents the kernel function, and g represents the linearized polynomial g(x) shown in expression (2). Specifically, assume that there exists a non-zero make Here, rank(g) represents the matrix rank of the codeword corresponding to the linearized polynomial g(x). Using proof by contradiction, it is assumed that there exists a non-zero codeword whose rank is less than a preset minimum distance d; then its corresponding self-adjoint linearized polynomial will have a kernel space whose dimension exceeds the upper bound. This polynomial is then subjected to a first finite field... With the second finite field After decomposing and analyzing the kernel space constraints under the two-layer structure, it can be deduced that a certain field element must be a square element, which directly and uniquely contradicts the setting that η is a non-square element. Thus, it is proved that the rank of all non-zero codewords is not less than d.

[0039] 3) Inequivalence with existing codes. Specifically, the definition of equivalence between symmetric rank-distance codes is as follows: two codes... Equivalent, of which, Represents the base domain Given an n-dimensional symmetric matrix space. If there exists... Invertible matrix Domain automorphism and symmetric matrices Then it can make For linear codes, it can be set that... .in, Represents the base domain The group consisting of all non-zero elements in the group. Represents the second finite field All reversible The general linear group formed by linear transformations. For automorphism mapping, Represents the base domain The automorphism group. An automorphism group is a group of groups that... Mapped to All double shots.

[0040] By analyzing the minimum and maximum degrees of the q-polynomials, it can be seen that all non-zero codewords in the Schmidt construction correspond to... - All polynomials contain a first-order term, and all non-zero codewords constructed in this invention... - Polynomials do not contain linear terms (because) Right now The number of times ,and (where k is not 0). This fundamental difference remains unchanged under equivalent transformations, therefore the two codes are not equivalent.

[0041] After the above proof, expression (1) actually represents a set of symmetric bilinear types with multiple elements, where each element is a symmetric bilinear type. In practical applications, maximal linear symmetric rank distance codes can be constructed according to actual needs. For example, if the matrix order of the maximal linear symmetric rank distance code is required to be 8 and the minimum rank distance is required to be 4, n can be set to 8 and d to 4 in expression (1), and adjustments can be made according to actual needs. , , By using parameters such as ..., the corresponding first target symmetric bilinear set can be obtained. Transforming the first target symmetric bilinear set, the first maximal linear symmetric rank distance code can be obtained, and the first maximal linear symmetric rank distance code includes codewords (i.e., symmetric matrices) with a square matrix order of 8 and a minimum rank distance of 4. For example, if the square matrix order of the maximal linear symmetric rank distance code is required to be 10 and the minimum rank distance is required to be 6, n can be set to 10 and d to 6 in expression (1), and adjusted according to actual needs. , , By obtaining parameters such as these, we can obtain the corresponding second-target symmetric bilinear type set. Transforming the second-target symmetric bilinear type set yields the second-maximum linear symmetric rank-distance code, which includes codewords from a matrix of order 10 and a minimum rank distance of 6.

[0042] If the values ​​of 's' in the two constructions are not equal under modulo n, then the maximal linear symmetric rank distance codes obtained from the two constructions are not equivalent. For example, suppose n=6. According to the principle that n and 's' are coprime, the value of 's' in the first construction can be 5, and the value of 's' in the second construction can be 7. Since 7(mod 6)=1 and 5(mod 6)=5, they are not equal, therefore the maximal linear symmetric rank distance codes obtained from the two constructions are not equivalent. 'mod' represents the modulo operation.

[0043] If the value of s in the two constructions is equal under modulo n, it can be determined through the parameter. The maximal linear symmetric rank-distance codes generated by these two constructions are not equivalent. Specifically, this depends on the number of elements in the base field. In the case where the values ​​of s in the two constructions are equal under modulo n, then in the two constructions... When the value of satisfies the following two preset conditions, it can be determined that the maximal linear symmetric rank distance codes obtained by the two constructions are not equivalent.

[0044] 1) And exist , , , making ; 2) And exist , , , making .

[0045] In summary, in the symmetric bilinear set shown in expression (1), firstly, all codewords in the Schmidt construction contain... As the principal term, and the associated linearized polynomial contains a linear term, the first term of this application does not contain a linear term (i.e., the first term...). middle (where k is not 0), which is fundamentally different from Schmidt's construction, making the maximal linear symmetric rank distance code constructed in this application not equivalent to the maximal linear symmetric rank distance code constructed by Schmidt. The above In this context, Tr is the trace function that maps the elements of the extended field back to the base field. Let x be a constant, and let x and y be variables.

[0046] Secondly, the construction method of this application is applicable to even numbers n greater than 4 and even numbers d less than n. That is, within these parameter intervals, a novel symmetric extremum code construction method different from the Schmidt construction is proposed. At the same time, compared with the Schmidt construction, this application increases the number of polynomial terms and introduces a two-field construction to jointly destroy the matrix regular algebra structure, thereby increasing the difficulty of decryption.

[0047] Thirdly, the second aspect of this application includes symmetric terms, and the number of symmetric terms is determined by the order of the symmetric matrix and the minimum rank distance. In this way, different code structures with different structural complexities can be obtained for different orders of the symmetric matrix and the minimum rank distance, thereby ensuring the diversity of code structures.

[0048] Fourthly, since the exponent of the symmetric term includes s, and s is coprime to the order of the symmetric matrix, different exponent orbitals can be generated for different s, resulting in completely different q-polynomial distributions, thus ensuring the diversity of code structure.

[0049] Fifthly, the coefficients of the first and third terms lie in the first finite field, the coefficient of the second term lies in the second finite field, and the first finite field is the base field. The nth extension of the base field, with the second finite field as the base field, allows the coefficients of different terms to have different algebraic properties, thereby increasing the diversity of code structures.

[0050] Sixthly, non-square element parameters are introduced in the third item. After that, non-square element parameters Combining with the symmetric term of the second term, it can generate a code structure that is completely different from the traditional construction, thus enriching the code structure.

[0051] Based on the above description, this application provides an encoding method that can be used to construct a maximal linear symmetric rank distance code. The encoding method can be applied to electronic devices. Electronic devices may include, but are not limited to, tablet computers, desktop computers, and laptop computers. (See also...) Figure 1 This is a flowchart illustrating the encoding method provided in some embodiments of this application. Figure 1 In this context, the encoding method includes the following steps: Step S101: Obtain communication data and encoding parameters, wherein the codeword used for encoding is a symmetric square matrix of even order, and the encoding parameters include the order of the square matrix.

[0052] Specifically, the communication data is the data to be encoded.

[0053] The electronic device implementing the method of this application can display a human-computer interaction interface and receive encoded parameters through the human-computer interaction interface, or the electronic device can obtain preset parameters from a specified storage area as encoded parameters. This application does not limit the method of obtaining encoded parameters.

[0054] Step S102: Construct a symmetric bilinear form set corresponding to the order of the square matrix. Each element in the symmetric bilinear form set includes a first term, a second term, and a third term. The coefficients of the first and third terms are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is the nth extension of the base field. The exponent of the first term is based on the number of elements in the base field. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power.

[0055] Specifically, the so-called construction is to substitute the programming parameters into expression (1) to obtain the corresponding symmetric bilinear set. For the first, second and third terms, please refer to the relevant descriptions above, which will not be repeated here.

[0056] Step S103: Generate a target code based on the elements in the symmetric bilinear set, and use the target code to encode the communication data.

[0057] Specifically, since there is a one-to-one correspondence between symmetric bilinear types and codewords (i.e., symmetric square matrices), transforming the elements in the symmetric bilinear type set yields the corresponding target code. Once the target code is obtained, communication data can be encoded based on it. Using rank-distance code encoding is a conventional technique, and will not be elaborated upon here.

[0058] In summary, in the technical solutions of some embodiments of this application, firstly, the number of times the first item is set to... This fundamentally differs from Schmidt's construction, making the maximal linear symmetric rank distance code constructed in this application inequivalent to Schmidt's maximal linear symmetric rank distance code. Secondly, this application includes the first, second, and third terms, providing space for different code structures and avoiding the degeneration into a single two-term term as seen in Schmidt's construction, thus ensuring code structure diversity. Finally, the coefficients of the first and third terms lie in the first finite field, the coefficient of the second term lies in the second finite field, and the first finite field is the base field. The nth extension of the base field, with the second finite field as the base field, allows the coefficients of different terms to have different algebraic properties, thereby increasing the diversity of code structures.

[0059] In some embodiments, the encoding parameters further include minimum rank distance, and the coefficients of the second term include at least one sub-coefficient; constructing a symmetric bilinear set corresponding to the order of the square matrix includes: The number of symmetric terms is determined based on the order of the square matrix and the minimum rank distance. Based on the number of symmetrical terms, set symmetrical terms in the second term; The sub-coefficients are used as the coefficients of the symmetric terms, and there is a one-to-one correspondence between the sub-coefficients and the symmetric terms; The second term is constructed by adding together the multiple symmetrical terms of the second term.

[0060] Referring to expression (1), the coefficient of the second term is... ~ The sub-coefficient is one of the coefficients. The number of symmetric terms is The summation term is obtained by adding together the multiple symmetrical terms of the second term.

[0061] In the above embodiments, the second term includes symmetric terms, and the number of symmetric terms is determined by the order of the symmetric matrix and the minimum rank distance. In this way, different code structures with different structural complexities can be obtained for different orders of the symmetric matrix and the minimum rank distance, thereby ensuring the diversity of code structures.

[0062] In some embodiments, the encoding parameters further include structure parameter values ​​that are coprime to the order of the square matrix, and the symmetric terms of the second term have symmetric term indices; setting symmetric terms in the second term includes: Based on the order of the square matrix and the index of the symmetric terms, generate distinct exponential term variables for each symmetric term; Using structural parameter values ​​as common factors and exponential variable as distinguishing factors, exponential terms are set for each symmetric term in the second term.

[0063] Referring to expression (1), the structural parameter value is s, and the exponential term variable is... Where i is the index of the symmetric term, and k is... Where n is the order of the square matrix. The exponents of each symmetric term in the second term are set to... .

[0064] In the above embodiments, since the symmetric term index is unique, using the exponent term variable as a distinguishing factor can ensure that the exponent terms of different symmetric terms are different, thereby ensuring the diversity of the code structure. Furthermore, using the structural parameter value as a common factor can ensure that the exponent terms of different symmetric terms are distinct and linearly independent.

[0065] In some embodiments, the encoding parameters further include the minimum rank distance and a structure parameter value coprime to the order of the square matrix. Constructing a symmetric bilinear set corresponding to the order of the square matrix includes: Set a symmetrical term in the third item; The adjustment parameter values ​​are determined based on the minimum rank distance and the structural parameter values; Using the number of elements in the base field as the base and the adjustment parameter value as the exponent, an exponent term is set for the symmetric term in the third term.

[0066] Referring to expression (1), the minimum rank distance is d, the structural parameter is s, and the adjustment parameter is... The symmetrical terms in the third term are set as follows: The values ​​of symmetric terms change dynamically with d and s, which can improve the diversity of code structure.

[0067] In some embodiments, when the structural parameter value is a first parameter value, the elements in the symmetric bilinear set are used to generate a first code, and when the structural parameter value is a second parameter value, the elements in the symmetric bilinear set are used to generate a second code. When the values ​​of the first parameter and the second parameter are not equal under modulo n operation, the first code and the second code are non-equivalent codes.

[0068] Referring to expression (1), the structural parameter value is s. During the encoding process, in order to avoid the generation of equivalent codes, the value of s can be planned in advance to avoid the situation where the absolute value of s is the same in two different constructions.

[0069] In some embodiments, the encoding parameters further include coefficient adjustment parameter values, wherein the coefficient adjustment parameter values ​​are located in the second finite field and are non-square elements of the second finite field; the method further includes: Based on the coefficient adjustment parameter value, the coefficient of the third term is adjusted. When the coefficient adjustment parameter value is the third parameter value, the elements in the symmetric bilinear set are used to generate the third code, and when the coefficient adjustment parameter value is the fourth parameter value, the elements in the symmetric bilinear set are used to generate the fourth code.

[0070] In some embodiments, when the values ​​of the first parameter and the second parameter are equal under modulo n operation, if the values ​​of the third parameter and the fourth parameter satisfy a preset condition, then the third code and the fourth code are non-equivalent codes.

[0071] Referring to expression (1), the coefficient adjustment parameter value is... . It can be coordinated with the structural parameter value s. If, in two different constructions, the absolute value of s is unavoidably the same, it can be adjusted. The value of makes the different construction times The value meets the preset conditions, thus improving the reliability of the solution and minimizing the generation of equivalent code. For the preset conditions, please refer to the relevant description for expression (1), which will not be repeated here.

[0072] See also Figure 2 The diagram below illustrates the encoding and decoding process for some embodiments of this application. Figure 2In this process, devices such as wireless communication terminals, base stations, and cloud storage servers can send the communication data to be encoded and the encoding parameters to the encoding / decoding platform. The encoding / decoding platform constructs a symmetric bilinear set based on the encoding parameters and expression (1), obtains the corresponding target code, encrypts the communication data based on the target code, and then returns the encrypted communication data to the wireless communication terminal, base station, and cloud storage server. Similarly, after receiving the undecoded communication data, the wireless communication terminal, base station, and cloud storage server can send the undecoded communication data to the encoding / decoding platform for decoding.

[0073] See also Figure 3 This is a schematic diagram of an encoding device provided in some embodiments of this application. The encoding device includes: The data acquisition module 301 is used to acquire communication data and encoding parameters, wherein the codeword used for encoding is an even-order symmetric square matrix, and the encoding parameters include the order of the square matrix; Set construction module 302 is used to construct a symmetric bilinear set corresponding to the order of a square matrix. Each element in the symmetric bilinear set includes a first term, a second term, and a third term. The coefficients of the first and third terms are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is the nth extension of the base field. The exponent of the first term is based on the number of elements in the base field. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power. The encoding module 303 is used to generate a target code based on the elements in the symmetric bilinear set, and to encode the communication data using the target code.

[0074] In some embodiments, the encoding parameters further include the minimum rank distance, and the coefficients of the second term include at least one sub-coefficient; the set construction module 302 is specifically used for: The number of symmetric terms is determined based on the order of the square matrix and the minimum rank distance. Based on the number of symmetrical terms, set symmetrical terms in the second term; The sub-coefficients are used as the coefficients of the symmetric terms, and there is a one-to-one correspondence between the sub-coefficients and the symmetric terms; The second term is constructed by adding together the multiple symmetrical terms of the second term.

[0075] In some embodiments, the encoding parameters further include structure parameter values ​​that are coprime to the order of the square matrix, and the symmetric terms of the second term have symmetric term indices; the set construction module 302 is specifically used for: Based on the order of the square matrix and the index of the symmetric terms, generate distinct exponential term variables for each symmetric term; Using structural parameter values ​​as common factors and exponential variable as distinguishing factors, exponential terms are set for each symmetric term in the second term.

[0076] In some embodiments, the encoding parameters further include the minimum rank distance and a structure parameter value coprime to the order of the square matrix; the set construction module 302 is specifically used for: Set a symmetrical term in the third item; The adjustment parameter values ​​are determined based on the minimum rank distance and the structural parameter values; Using the number of elements in the base field as the base and the adjustment parameter value as the exponent, an exponent term is set for the symmetric term in the third term.

[0077] In some embodiments, when the structural parameter value is a first parameter value, the elements in the symmetric bilinear set are used to generate a first code, and when the structural parameter value is a second parameter value, the elements in the symmetric bilinear set are used to generate a second code. When the values ​​of the first parameter and the second parameter are not equal under modulo n operation, the first code and the second code are non-equivalent codes.

[0078] In some embodiments, the encoding parameters further include coefficient adjustment parameter values, which are located in the second finite field and are non-square elements of the second finite field; the set construction module 302 is specifically used for: Based on the coefficient adjustment parameter value, the coefficient of the third term is adjusted. When the coefficient adjustment parameter value is the third parameter value, the elements in the symmetric bilinear set are used to generate the third code, and when the coefficient adjustment parameter value is the fourth parameter value, the elements in the symmetric bilinear set are used to generate the fourth code.

[0079] In some embodiments, when the values ​​of the first parameter and the second parameter are equal under modulo n operation, if the values ​​of the third parameter and the fourth parameter satisfy a preset condition, then the third code and the fourth code are non-equivalent codes.

[0080] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0081] In this embodiment, the encoding device is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0082] Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application, such as... Figure 4As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 4 Take a processor 10 as an example.

[0083] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0084] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0085] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0086] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0087] This application provides a computer program product including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the method of any embodiment of this application.

[0088] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. An encoding method, characterized in that, The method includes: Acquire communication data and encoding parameters, wherein the codeword used for encoding is a symmetric square matrix of even order, and the encoding parameters include the order of the square matrix; Construct a symmetric bilinear set corresponding to the order of the square matrix. Each element in the symmetric bilinear set includes a first term, a second term, and a third term. The coefficients of the first term and the third term are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is an nth-order extension of the base field, and the exponent of the first term uses the number of elements in the base field as its base. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power. Based on the elements in the symmetric bilinear set, a target code is generated, and the target code is used to encode the communication data.

2. The method according to claim 1, characterized in that, The encoding parameters also include the minimum rank distance, and the coefficients of the second term include at least one sub-coefficient; The construction of the symmetric bilinear set corresponding to the order of the square matrix includes: The number of symmetric terms is determined based on the order of the square matrix and the minimum rank distance. According to the number of symmetrical terms, set symmetrical terms in the second term; The sub-coefficients are used as coefficients of the symmetric terms, and the sub-coefficients correspond one-to-one with the symmetric terms; The construction of the second term is completed by adding together the multiple symmetrical terms of the second term.

3. The method according to claim 2, characterized in that, The encoding parameters also include structural parameter values ​​that are coprime to the order of the square matrix, and the symmetric terms of the second term have symmetric term indices; The step of setting a symmetrical term in the second term includes: Based on the order of the square matrix and the index of the symmetric terms, generate distinct exponential term variables for each of the symmetric terms. Using the structural parameter values ​​as common factors and the exponential term variables as distinguishing factors, exponential terms are set for each symmetric term in the second term.

4. The method according to claim 1, characterized in that, The encoding parameters also include the minimum rank distance and a structural parameter value that is coprime to the order of the square matrix; The construction of the symmetric bilinear set corresponding to the order of the square matrix includes: A symmetrical term is set in the third term; Based on the minimum rank distance and the structural parameter values, the adjustment parameter values ​​are determined; Using the number of elements in the base domain as the base and the adjustment parameter value as the exponent, an exponent term is set for the symmetric term in the third term.

5. The method according to claim 3 or 4, characterized in that, When the structural parameter value is the first parameter value, the elements in the symmetric bilinear set are used to generate the first code; and when the structural parameter value is the second parameter value, the elements in the symmetric bilinear set are used to generate the second code. Wherein, when the values ​​of the first parameter and the second parameter are not equal under modulo n operation, the first code and the second code are non-equivalent codes.

6. The method according to claim 5, characterized in that, The encoding parameters further include coefficient adjustment parameter values, which are located in the second finite field and are non-square elements of the second finite field; the method further includes: Based on the coefficient adjustment parameter value, the coefficient of the third term is adjusted, wherein when the coefficient adjustment parameter value is the third parameter value, the elements in the symmetric bilinear set are used to generate the third code, and when the coefficient adjustment parameter value is the fourth parameter value, the elements in the symmetric bilinear set are used to generate the fourth code.

7. The method according to claim 6, characterized in that, If the first parameter value and the second parameter value are equal under modulo n operation, and if the third parameter value and the fourth parameter value satisfy a preset condition, then the third code and the fourth code are non-equivalent codes.

8. An encoding device, characterized in that, The device includes: The data acquisition module is used to acquire communication data and encoding parameters, wherein the codeword used for encoding is a symmetric square matrix of even order, and the encoding parameters include the order of the square matrix; A set construction module is used to construct a symmetric bilinear set corresponding to the order of the square matrix. Each element in the symmetric bilinear set includes a first term, a second term, and a third term. The coefficients of the first term and the third term are located in a first finite field, and the coefficient of the second term is located in a second finite field. The first finite field is the base field. The second finite field is an nth-order extension of the base field, and the exponent of the first term uses the number of elements in the base field as its base. As an exponent, n is the order of the square matrix, and the number of elements in the base field is an odd prime power. The encoding module is used to generate a target code based on the elements in the symmetric bilinear set, and to encode the communication data using the target code.

9. A computer device, characterized in that, include: A memory and a processor are communicatively connected, the memory stores computer instructions, and the processor executes the encoding method of any one of claims 1 to 7 by executing the computer instructions.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a computer to perform the encoding method according to any one of claims 1 to 7.

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