A data encoding system and method based on a simplex complex homogenization linear code

Abstract

This invention discloses a data encoding system and method based on simplicated complex homogeneous linear codes. The system includes: a parameter initialization module for initializing the construction parameters of an n-ary multivariable function F; a function definition module for generating the multivariable function F based on the construction parameters; and a definition set extraction module for constructing a definition set D. F ; Linear code generation module, used to generate linear codes according to the definition set D F This invention employs an inner product mapping to construct a basic p-ary linear code corresponding to the defined set; a homogenization processing module is used to homogenize the multivariable function F to obtain an (n+1)-ary homogeneous function; and a homogenized code generation module is used to generate a homogenized definition set based on the homogenized function, and then generate a homogenized p-ary linear code based on this set. This invention solves the problems of existing p-ary linear code construction techniques being complex in structure, having uncontrollable parameters, or being difficult to analyze weight distribution, leading to difficulties in efficient deployment in engineering.

Description

Technical Field

[0001] This invention belongs to the field of information technology, and in particular relates to a data encoding system and method based on simple complex homogeneous linear codes. Background Technology

[0002] In modern information technology systems, digital communication networks and massive data storage systems are critical infrastructures supporting societal operations. Reliable transmission and secure storage of information within these systems are the cornerstones ensuring the normal operation of various applications. However, noise, interference in physical channels, and inherent defects in storage media inevitably introduce data errors, seriously threatening system stability and data integrity. To address this problem, error-correcting coding technology has emerged. Its core idea is to systematically add redundant information to the original data, enabling the receiving end to automatically detect and correct errors within a certain range, thereby achieving reliable data exchange over unreliable physical media.

[0003] With the development of technologies such as multi-level modulation and multi-level storage, non-binary linear codes, especially p-ary linear codes over the prime field, have become an important research and application direction due to their superior symbol matching characteristics. Currently, the construction methods for p-ary linear codes still have significant shortcomings: First, some methods rely on random or empirical design, making it difficult to precisely control and predict code parameters, and thus unable to flexibly adapt to the reliability requirements of specific scenarios; second, many constructions with good theoretical boundaries (such as optimal codes approaching the Griesmer bound) have complex structures and difficult weight distribution analysis, leading to high costs for engineering implementation and performance evaluation. Existing technologies lack a systematic construction scheme with a clear structure, controllable parameters, and easily theoretically derived weight distribution, which restricts its efficient deployment in engineering.

[0004] To address the challenges of efficient deployment in engineering due to the complex structure, uncontrollable parameters, or difficulty in weight distribution analysis of existing p-ary linear code construction techniques, a data encoding system and method based on simple complex homogeneous linear codes are proposed. Summary of the Invention

[0005] This invention proposes a data encoding system and method based on simple complex homogeneous linear codes, which at least solves the problems of existing p-ary linear code construction techniques being complex in structure, having uncontrollable parameters, or being difficult to analyze weight distribution, making them difficult to deploy efficiently in engineering.

[0006] According to an embodiment of the present invention, a data encoding system based on simple complex homogeneous linear codes is provided, comprising:

[0007] The parameter initialization module is used to set the prime number parameter p and the variable dimension n in a finite field, and to initialize the construction parameters of the n-variable function F.

[0008] The function definition module is used to generate the multivariable function F based on the construction parameters;

[0009] The definition set extraction module is used to extract the set of exponential vectors corresponding to the non-zero terms of the multivariable function F, thereby constructing the definition set D. F ;

[0010] The linear code generation module is used to generate linear codes based on the definition set D. F The basic p-ary linear code corresponding to the defined set is constructed by inner product mapping;

[0011] The homogenization module is used to introduce homogenous variables and perform homogenization operations on the multivariable function F to obtain an (n+1)-ary homogenous function.

[0012] The homogenization code generation module is used to generate a homogenization definition set based on the homogenization function, and generate a homogenized p-ary linear code based on this set.

[0013] In a preferred embodiment, the construction parameters of the multivariable function F include a set of variables, an exponent range, and a coefficient value space; the generation of the multivariable function F based on the construction parameters is based on defining an n-variable multivariable function F on a finite field, wherein the function terms consist of one or more monomials and their corresponding coefficients.

[0014] In a preferred embodiment, the definition set extraction module is configured as follows:

[0015] Select a simple complex structure, wherein the simple complex structure includes one based on a vector covering partial order relation or a vector support set inclusion relation;

[0016] In the simple complex structure, a sub-complex generated by a finite number of maximal elements is selected;

[0017] The set of vectors in the subcomplex is taken as the definition set D. F .

[0018] In a preferred embodiment, the homogenization processing module includes:

[0019] Introducing a new homogeneous variable x n+1 ;

[0020] Homogenization of the multivariable function F yields an (n+1)-variable homogeneous function. .

[0021] In a preferred embodiment, the homogeneous coding generation module includes:

[0022] Calculate the homogenized definition set corresponding to the homogenous function; the homogenized definition set is the definition set D. FThe set after adding homogeneous coordinates to the elements in the middle;

[0023] Constructing the corresponding p-ary linear code based on the homogenization definition set is called a homogenized p-ary linear code.

[0024] In a preferred embodiment, it further includes a complement encoding module, used for:

[0025] Calculate the complement of the homogenized definition set in the universal set space;

[0026] Construct a p-ary linear code corresponding to the complement based on the complement;

[0027] Calculate the code length and weight distribution of the p-ary linear code corresponding to the complement based on the algebraic structure of the complement.

[0028] According to another embodiment of the present invention, a data encoding apparatus based on a simple complex homogeneous linear code is provided, comprising:

[0029] The data coding system based on simple complex homogeneous linear codes as described above;

[0030] The data interface is used to receive source data to be encoded.

[0031] An encoding processor is used to encode the source data by calling the p-ary linear code generated by the data encoding system to obtain a codeword sequence;

[0032] The output interface is used to send the codeword sequence to a communication channel or write it to a storage medium.

[0033] According to another embodiment of the present invention, a communication device is provided, comprising:

[0034] The data encoding device based on the simple complex homogeneous linear code described above;

[0035] A modulation and demodulation unit is used to modulate the codeword sequence into a signal suitable for channel transmission;

[0036] A transceiver unit is used to send or receive the signal.

[0037] According to another embodiment of the present invention, a data encoding method based on simplicial homogeneous linear codes is provided, comprising:

[0038] Initialize the construction parameters of an n-variable function F over a finite field;

[0039] The multivariable function F is generated based on the construction parameters;

[0040] Extract the set of exponential vectors corresponding to the non-zero terms based on the coefficients of the multivariable function F, and construct the definition set D accordingly. F ;

[0041] According to the definition set D F The basic p-ary linear code corresponding to the defined set is constructed by inner product mapping;

[0042] By introducing homogeneous variables, the multivariable function F is homogenized to obtain an (n+1)-variable homogeneous function.

[0043] A homogenized definition set is generated based on the homogenized function, and a homogenized p-ary linear code is generated based on this.

[0044] According to another embodiment of the present invention, a computer-readable storage medium is provided that stores a computer program for electronic data interchange, wherein the computer program causes a computer to execute the data encoding method based on simple complex homogeneous linear code as described above.

[0045] The advantages of the data encoding system and method based on simple complex homogeneous linear codes of the present invention are:

[0046] (1) By using multivariable functions or simple complex structures to generate the definition set, compared with the traditional random selection or empirical construction method, the initial parameters of the code can be controlled in a precise and structured manner, so as to design linear codes that meet specific code length and dimension requirements.

[0047] (2) Introducing a homogenization mapping that includes newly added homogenous variables, constructing a homogenization definition set and homogenization code, compared with the linear code constructed directly using the original definition set, can achieve the effect of transforming complex structures in non-homogeneous spaces into more regular and symmetrical structures in high-dimensional homogenous spaces, laying a unified framework for subsequent accurate mathematical analysis.

[0048] (3) Based on the complement of the homogenization definition set, construct the complement code and give an explicit calculation method for its weight distribution. Compared with the traditional method that requires complex combination calculation or affine space decomposition to analyze code weight, it can achieve the effect of directly and efficiently determining the weight distribution of the complement code by only the weight distribution of the original homogenized code, which greatly simplifies the performance analysis and evaluation process.

[0049] (4) Using the simple complex as a specific algebraic structure as a concrete implementation of generating the definition set, compared with general or abstract function construction, can achieve the effect of more intuitively associating the code weight of the linear code with the surface vector of the complex by utilizing the clear combinatorial and topological properties of the simple complex, thereby enabling in-depth analysis of the error correction performance of the code from a geometric and combinatorial perspective.

[0050] (5) The systematic construction chain from the definition set to the homogenized definition set and then to the complement set can achieve the effect of generating a series of "code families" with inherent algebraic correlation compared with isolated and scattered single code construction schemes. This means that linear codes with different redundancies can be generated under the same construction framework, providing system designers with a variety of coding options with adjustable parameters and traceable performance, which can help reduce the engineering implementation difficulty of the technical solution. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the data encoding system structure based on simple complex homogeneous linear codes according to an embodiment of the present invention.

[0052] Figure 2 This is a structural diagram of a data encoding device based on a simple complex homogeneous linear code according to an embodiment of the present invention.

[0053] Figure 3 This is a structural diagram of a communication device according to an embodiment of the present invention.

[0054] Figure 4 This is a flowchart of a data encoding method based on a simple complex homogeneous linear code according to an embodiment of the present invention.

[0055] Figure 5 This is a flowchart of sub-step S03' of the data encoding method based on simple complex homogeneous linear codes in an embodiment of the present invention.

[0056] Figure 6 This is a flowchart of sub-step S05 of the data encoding method based on simple complex homogeneous linear code in an embodiment of the present invention.

[0057] Figure 7 This is a flowchart of sub-step S06 of the data encoding method based on simple complex homogeneous linear codes in an embodiment of the present invention.

[0058] Figure 8 This is a flowchart of additional step S07 of the data encoding method based on simple complex homogeneous linear code in an embodiment of the present invention. Detailed Implementation

[0059] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and modifications without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0060] According to an embodiment of the present invention, a data encoding system based on simple complex homogeneous linear codes is provided, and the system structure diagram is shown below. Figure 1 As shown, it includes:

[0061] The parameter initialization module is used to set the prime number parameter p and the variable dimension n in a finite field, and to initialize the construction parameters of the n-variable function F.

[0062] The function definition module is used to generate the multivariable function F based on the construction parameters;

[0063] The definition set extraction module is used to extract the set of exponential vectors corresponding to the non-zero terms of the multivariable function F, thereby constructing the definition set D. F ;

[0064] The linear code generation module is used to generate linear codes based on the definition set D. F The basic p-ary linear code corresponding to the defined set is constructed by inner product mapping;

[0065] The homogenization module is used to introduce homogenous variables and perform homogenization operations on the multivariable function F to obtain an (n+1)-ary homogenous function.

[0066] The homogenization code generation module is used to generate a homogenization definition set based on the homogenization function, and generate a homogenized p-ary linear code based on this set.

[0067] In a preferred embodiment, the construction parameters of the multivariable function F include a set of variables, an exponent range, and a coefficient value space. The generation of the multivariable function F based on the construction parameters involves defining an n-variable multivariable function F over a finite field, where each function term consists of one or more monomials and their corresponding coefficients. In this embodiment, within a finite field... We select a prime number parameter p and a variable dimension n, where p ≥ 2 and n is a positive integer.

[0068] Based on the expected code length, dimension, and minimum distance requirements for constructing a linear code, the range of exponent values ​​and coefficient selection rules for the multivariable function are predetermined, thereby enabling the construction of a linear code within a finite field. Let an n-ary multivariable function F be defined, and its expression is shown in equation (1).

[0069] (1)

[0070] in , represents a vector in a finite field, with coefficients .

[0071] By selecting the positions of the non-zero coefficient terms, the support set of the n-variable function F can exhibit the expected combinatorial properties in its algebraic structure.

[0072] In a preferred embodiment, the definition set extraction module is configured to: form a definition set by assembling the exponential vectors corresponding to all non-zero coefficients in the above-mentioned n-variable multivariable function F. .

[0073] In another preferred embodiment, the definition set extraction module is configured as follows:

[0074] Select a simple complex structure, wherein the simple complex structure includes one based on a vector covering partial order relation or a vector support set inclusion relation;

[0075] In the simple complex structure, a sub-complex generated by a finite number of maximal elements is selected;

[0076] The set of vectors in the subcomplex is taken as the definition set D. F .

[0077] In this embodiment, a simplicial complex structure based on vector covering partial order relation or a simplicial complex structure based on vector support set inclusion relation is selected; the corresponding simplicial complex is generated from a finite number of maximal elements. ,make That is, we obtain the definition set D. F .

[0078] In a preferred embodiment, the linear code generation module is configured as follows:

[0079] Based on the definition set D F In vector space The standard inner product mapping is introduced above, which applies to any information vector. Constructing codewords This yields a p-ary linear code. This construction method allows the code length of the linear code to be determined by the definition set D. F The size of the code is directly determined by the linear span of the definition set, and the dimension of the code is related to the linear span of the definition set, thus providing a direct algebraic means for parameter control.

[0080] In a preferred embodiment, the homogenization processing module includes:

[0081] Introducing a new homogeneous variable x n+1 ;

[0082] Homogenization of the multivariable function F yields an (n+1)-variable homogeneous function. .

[0083] In this embodiment, to further enhance the controllability of the code parameters and introduce projective geometry, the multivariable function F is homogenized based on the above. Specifically, a new homogenous variable x is introduced. n+1 And let the homogeneous degree of the function be equal to the total degree of the original function. Thus, the corresponding (n+1)-element homogeneous function is constructed. Its structure is shown in equation (2).

[0084] (2)

[0085] In this homogenization process, homogeneous variables are introduced into each monomial in the original function by supplementing its degree, so that the resulting function maintains homogeneity in algebraic structure.

[0086] In a preferred embodiment, the homogeneous coding generation module includes:

[0087] Calculate the homogenized definition set corresponding to the homogenous function; the homogenized definition set is the definition set D. F The set after adding homogeneous coordinates to the elements in the middle;

[0088] Constructing the corresponding p-ary linear code based on the homogenization definition set is called a homogenized p-ary linear code.

[0089] In this embodiment, a homogenization definition set is further constructed corresponding to the homogenization function. As shown in equation (3).

[0090] (3)

[0091] This homogenization definition set It can be viewed as an improvement based on the original set of definitions after introducing homogeneous coordinates.

[0092] Based on the homogenization definition set Following the same inner product mapping method as described above, construct homogeneous p-ary linear codes. As shown in equation (4).

[0093] (4)

[0094] The homogeneous code has a code length equal to that of the original code, its dimension does not exceed n+1, and it can be explicitly calculated through the linear independence of the row vectors in the generator matrix. Due to the introduction of the homogeneous structure, this type of linear code exhibits a high degree of regularity in weight distribution, making it possible to analyze the minimum distance using algebraic methods and, with appropriate parameter selection, reach or approximate the Griesmer bound.

[0095] In a preferred embodiment, it further includes a complement encoding module, used for:

[0096] Calculate the complement of the homogenized definition set in the universal set space;

[0097] Construct a p-ary linear code corresponding to the complement based on the complement;

[0098] Calculate the code length and weight distribution of the p-ary linear code corresponding to the complement based on the algebraic structure of the complement.

[0099] In this embodiment, in the universal space of the homogenized definition set In, construct its complement. Based on this complement, the corresponding p-ary linear code is constructed using the same inner product mapping method as described above. This is called the two's complement. In this embodiment, the code length of the two's complement is... Its codeword weight can be directly calculated from the weight of the homogeneous code through a complementary relationship, that is... , where δ is the Kronecker function. This relationship allows the weight distribution of the two's complement to be obtained without re-enumerating, significantly reducing the analysis complexity.

[0100] Based on the above embodiments, examples are provided for illustration:

[0101] Choose p=3 (prime field) ), n=3 (number of variables), the simplex complex Δ is a complex generated by a maximal element (1,1,0), then the definition set Δ={(0,0,0),(1,0,0),(0,1,0),(1,1,0)}, n-variable function After homogenization, we obtain a homogeneous function of (n+1) variables. Homogeneity definition set Δ h ={(0,0,0,2),(1,0,0,1),(0,1,0,1),(1,1,0,0)}, the homogeneous code has parameters [4,3,2], reaching the Griesmer bound. Tables 1 and 2 show some homogeneous codes, their complements, and their complements obtained based on the above method.

[0102] Table 1. Data of codes generated from simple complexes based on vector covering partial order relations.

[0103]

[0104] Table 2 Data of codes generated from simple complexes based on vector support set inclusion relations

[0105]

[0106] According to another embodiment of the present invention, a data encoding device based on a simple complex homogeneous linear code is provided, the structure of which is shown in the figure below. Figure 2 As shown, it includes:

[0107] The data coding system based on simple complex homogeneous linear codes as described above;

[0108] The data interface is used to receive source data to be encoded.

[0109] An encoding processor is used to encode the source data by calling the p-ary linear code generated by the data encoding system to obtain a codeword sequence;

[0110] The output interface is used to send the codeword sequence to a communication channel or write it to a storage medium.

[0111] According to another embodiment of the present invention, a communication device is provided, the structural diagram of which is shown below. Figure 3 As shown, it includes:

[0112] The data encoding device based on the simple complex homogeneous linear code described above;

[0113] A modulation and demodulation unit is used to modulate the codeword sequence into a signal suitable for channel transmission;

[0114] A transceiver unit is used to send or receive the signal.

[0115] According to another embodiment of the present invention, a data encoding method based on simple complex homogeneous linear codes is provided, the flowchart of which is shown below. Figure 4 As shown, it includes:

[0116] Step S01: Initialize the construction parameters of the n-variable function F over the finite field;

[0117] Step S02: Generate the multivariable function F according to the construction parameters;

[0118] Step S03: Extract the set of exponential vectors corresponding to the non-zero terms based on the coefficients of the multivariable function F, and construct the definition set D accordingly. F ;

[0119] Step S04: According to the definition set D F The basic p-ary linear code corresponding to the defined set is constructed by inner product mapping;

[0120] Step S05: Introduce homogeneous variables and perform homogenization operation on the multivariable function F to obtain an (n+1)-variable homogeneous function;

[0121] Step S06: Generate a homogenization definition set based on the homogenization function, and generate a homogenized p-ary linear code based on this set.

[0122] In a preferred embodiment, the construction parameters of the multivariable function F include a set of variables, an exponent range, and a coefficient value space. The generation of the multivariable function F based on the construction parameters involves defining an n-variable multivariable function F over a finite field, where each function term consists of one or more monomials and their corresponding coefficients. In this embodiment, within a finite field... We select a prime number parameter p and a variable dimension n, where p ≥ 2 and n is a positive integer.

[0123] Based on the expected code length, dimension, and minimum distance requirements for constructing a linear code, the range of exponent values ​​and coefficient selection rules for the multivariable function are predetermined, thereby enabling the construction of a linear code within a finite field. Let an n-ary multivariable function F be defined, and its expression is shown in equation (1).

[0124] By selecting the positions of the non-zero coefficient terms, the support set of the n-variable function F can exhibit the expected combinatorial properties in its algebraic structure.

[0125] In a preferred embodiment, step S03 includes: forming a definition set by assembling the exponential vectors corresponding to all non-zero coefficients in the above-mentioned n-variable multivariable function F. .

[0126] Another preferred embodiment of step S03 is denoted as step S03', and the flowchart is as follows: Figure 5 As shown, the steps include:

[0127] Step S03'1: Select a simple complex structure, wherein the simple complex structure includes a vector covering partial order relation or a vector support set inclusion relation;

[0128] Step S03'2: Select a sub-complex generated by a finite number of maximal elements in the simple complex structure;

[0129] Step S03'3: Use the set of vectors in the subcomplex as the definition set D. F .

[0130] In this embodiment, a simplicial complex structure based on vector covering partial order relation or a simplicial complex structure based on vector support set inclusion relation is selected; the corresponding simplicial complex is generated from a finite number of maximal elements. ,make That is, we obtain the definition set D. F .

[0131] In a preferred embodiment, step S04 specifically includes:

[0132] Based on the definition set D F In vector space The standard inner product mapping is introduced above, which applies to any information vector. Constructing codewords This yields a p-ary linear code. This construction method allows the code length of the linear code to be determined by the definition set D. F The size of the code is directly determined by the linear span of the definition set, and the dimension of the code is related to the linear span of the definition set, thus providing a direct algebraic means for parameter control.

[0133] In a preferred embodiment, step S05 is illustrated in the flowchart below. Figure 6As shown, it includes:

[0134] Step S051: Introduce a new homogeneous variable x n+1 ;

[0135] Step S052: Perform homogenization on the multivariable function F to obtain an (n+1)-variable homogeneous function.

[0136] In this embodiment, to further enhance the controllability of the code parameters and introduce projective geometry, the multivariable function F is homogenized based on the above. Specifically, a new homogenous variable x is introduced. n+1 And let the homogeneous degree of the function be equal to the total degree of the original function. Thus, the corresponding (n+1)-element homogeneous function is constructed. Its structure is shown in equation (2).

[0137] In this homogenization process, homogeneous variables are introduced into each monomial in the original function by supplementing its degree, so that the resulting function maintains homogeneity in algebraic structure.

[0138] In a preferred embodiment, step S06 is illustrated in the flowchart below. Figure 7 As shown, it includes:

[0139] Step S061: Calculate the homogenized definition set corresponding to the homogenized function; the homogenized definition set is the definition set D. F The set after adding homogeneous coordinates to the elements in the middle;

[0140] Step S062: Construct the corresponding p-ary linear code based on the homogenization definition set, which is the homogenized p-ary linear code.

[0141] In this embodiment, a homogenization definition set is further constructed corresponding to the homogenization function. As shown in equation (3).

[0142] This homogenization definition set It can be viewed as an improvement based on the original set of definitions after introducing homogeneous coordinates.

[0143] Based on the homogenization definition set Following the same inner product mapping method as described above, construct homogeneous p-ary linear codes. As shown in equation (4).

[0144] The homogeneous code has a code length equal to that of the original code, its dimension does not exceed n+1, and it can be explicitly calculated through the linear independence of the row vectors in the generator matrix. Due to the introduction of the homogeneous structure, this type of linear code exhibits a high degree of regularity in weight distribution, making it possible to analyze the minimum distance using algebraic methods and, with appropriate parameter selection, reach or approximate the Griesmer bound.

[0145] In a preferred embodiment, step S07 is further included, as shown in the flowchart below. Figure 8 As shown, it includes:

[0146] Step S071: Calculate the complement of the homogenized definition set in the universal set space;

[0147] Step S072: Construct the p-ary linear code corresponding to the complement based on the complement;

[0148] Step S073: Calculate the code length and weight distribution of the p-ary linear code corresponding to the complement based on the algebraic structure of the complement.

[0149] In this embodiment, in the universal space of the homogenized definition set In, construct its complement. Based on this complement, the corresponding p-ary linear code is constructed using the same inner product mapping method as described above. This is called the two's complement. In this embodiment, the code length of the two's complement is... Its codeword weight can be directly calculated from the weight of the homogeneous code through a complementary relationship, that is... , where δ is the Kronecker function. This relationship allows the weight distribution of the two's complement to be obtained without re-enumerating, significantly reducing the analysis complexity.

[0150] According to another embodiment of the present invention, a computer-readable storage medium is provided that stores a computer program for electronic data interchange, wherein the computer program causes a computer to execute a data encoding method based on simple complex homogeneous linear codes as described in any of the above embodiments.

[0151] The methods described above according to the invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be stored as software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an AuIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses the code used to implement the processes shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the processes shown herein.

[0152] Of course, those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Any changes or modifications to the above embodiments that are within the scope of the present invention will fall within the protection scope of the present invention.

Claims

1. A data encoding system based on a simplex complex homogenized linear code, characterized by, The method comprises the following steps: A parameter initialization module is configured to set a prime number parameter p and a variable dimension n on a finite field, and initialize construction parameters of an n-ary multivariate function F; A function definition module is configured to generate the multivariate function F according to the construction parameters; a definition set extraction module configured to extract a set of index vectors corresponding to non-zero terms according to coefficients of the multivariate function F, so as to construct a definition set D F ; a linear code generating module, configured to generate a linear code corresponding to the definition set D according to the definition set D F , adopt an inner product mapping to construct a basic p-element linear code corresponding to the definition set A homogenization processing module is configured to introduce a homogeneous variable, and perform a homogenization operation on the multivariate function F to obtain an (n+1)-ary homogeneous function; A homogeneous code generation module is configured to generate a homogeneous definition set according to the homogeneous function, and generate a homogeneous p-ary linear code based on the homogeneous definition set.

2. The data encoding system based on a simplicial complex homogenized linear code according to claim 1, characterized in that, The construction parameters of the multivariate function F include a variable set, an index range, and a coefficient value space; and the multivariate function F is defined on a finite field based on the construction parameters, and a function term of the multivariate function F is composed of one or more monomials and corresponding coefficients.

3. The data encoding system based on a simplicial complex homogenized linear code according to claim 1, characterized in that, The definition set extraction module is configured to: select a simple complex structure, wherein the simple complex structure includes a vector cover partial order relationship or a vector support set inclusion relationship; select a sub-complex generated by a limited number of maximal elements in the simple complex structure; to set D F .

4. The data encoding system based on a simplicial complex homogenized linear code according to claim 1, characterized in that, The homogenization processing module comprises: Introducing new homogeneous variable x n+1 ; performing a homogenization operation on the multivariate function F to obtain an (n+1)-ary homogeneous function. 。 5. The data encoding system based on a simplicial complex homogenized linear code according to claim 1, characterized in that, The homogeneous code generation module comprises: computing a homogenized definition set corresponding to the homogeneous function; the homogenized definition set is a definition set D F the set after adding the homogeneous coordinates of the middle elements constructing a corresponding p-ary linear code based on the homogeneous definition set, that is, a homogeneous p-ary linear code.

6. The data encoding system based on a simplicial complex homogenized linear code according to claim 1, characterized in that, The method further comprises a complement set encoding module configured to: calculate a complement set of the homogeneous definition set in a full set space; construct a p-ary linear code corresponding to the complement set based on the complement set; calculate a code length and a weight distribution of the p-ary linear code corresponding to the complement set according to an algebraic structure of the complement set.

7. A data encoding device based on a simplicial complex homogeneous linear code, characterized by The method comprises the following steps: The data encoding system based on a simple complex homogenization linear code according to any one of claims 1 to 6; a data interface configured to receive source data to be encoded; an encoding processor configured to encode the source data by using a p-ary linear code generated by the data encoding system to obtain a codeword sequence; an output interface configured to send the codeword sequence to a communication channel or write the codeword sequence to a storage medium.

8. A communication device, characterized by The method comprises the following steps: The data encoding system based on a simple complex homogenization linear code according to claim 7; a modulation and demodulation unit configured to modulate the codeword sequence into a signal suitable for channel transmission; a transceiver unit configured to send or receive the signal.

9. A data encoding method based on a simplicial complex homogeneous linear code, characterized by, The method comprises the following steps: initialize construction parameters of an n-ary multivariate function F on a finite field; generate the multivariate function F according to the construction parameters; According to the coefficient of the multivariate function F, the index vector set corresponding to the non-zero term is extracted, so as to construct the definition set D F ; According to the definition set D F , an inner product mapping is used to construct a basis p-ary linear code corresponding to the definition set. introduce a homogeneous variable, and perform a homogenization operation on the multivariate function F to obtain an (n+1)-ary homogeneous function; generate a homogeneous definition set according to the homogeneous function, and generate a homogeneous p-ary linear code based on the homogeneous definition set.

10. A computer-readable storage medium storing a computer program for electronic data interchange, characterized in that, The computer program enables a computer to perform the method according to claim 9.

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