Binary linear code generation matrix reduction method and device based on lattice reduction algorithm

Abstract

The invention discloses a binary linear code generated matrix reduction method and a binary linear code generated matrix reduction device based on a lattice basis DeepLLL reduction algorithm. In the operation of selecting whether an Epipodal vector corresponding to any basis vector in a given generated matrix is the shortest non-zero vector under the action of a corresponding orthogonal projection, the Epipodal vector corresponding to any basis vector in the given generated matrix is a non-zero vector; all the base vectors ranked behind the original base vector are sequentially subjected to the same orthogonal projection effect and then are compared with the original base vector in pairs, so that the shortest non-zero Epipodal vectors under the orthogonal projection effect are sequentially found out, and the Hamming weight distribution of the Epipodal vectors is more balanced; in the operation of inserting the base vectors, the base vectors meeting the reduction conditions only need to be directly inserted into the corresponding sequence positions instead of being exchanged with the previous base vectors, so that the calculation efficiency in the matrix updating stage is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a method and device for reducing a binary linear code generation matrix based on a lattice DeepLLL reduction algorithm. Background Art

[0002] In recent years, with the continuous development of communication technology, the reduction algorithm of the generator matrix of linear codes has become an important part in the field of information transmission and data storage. This is mainly because the reduction algorithm of the generator matrix can greatly optimize the efficiency of the encoding and decoding process, and also help to design a more efficient and resource-efficient communication system. The generator matrix of a linear code is a common form used to describe the characteristics of the linear code itself. It can be constructed by adding the required row vector or column vector to a unit matrix. However, the generator matrix itself will become more complex as the amount of data in the communication system increases, resulting in a sharp increase in the cost of calculation and storage. Therefore, how to optimize the reduction algorithm of the generator matrix of linear codes has become an urgent problem to be solved in the field of information transmission. Summary of the invention

[0003] The present invention provides a method and device for reducing a binary linear code generation matrix based on a lattice DeepLLL reduction algorithm, so as to solve the problem of low processing efficiency of the existing linear code generation matrix reduction algorithm.

[0004] In a first aspect, the present invention provides a method for reducing a binary linear code generation matrix based on a lattice DeepLLL reduction algorithm, the method comprising:

[0005] Input an arbitrary generator matrix of a binary linear code, calculate the Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix;

[0006] Determine any Epipodal vector in the Epipodal matrix Is it the shortest non-zero Epipodal vector under the i-th orthogonal projection? If not, it means that there is a basis vector a j , whose length under the i-th orthogonal projection is shorter, the two basis vectors are judged by the Lovasz condition, and if yes, the generator matrix and its corresponding Epipodal matrix are output;

[0007] Perform Lovasz condition judgment on two basis vectors. If the condition is satisfied, then the basis vector a j Perform an XOR operation and then enter the basis vector a that satisfies the reduction condition j Perform basis reduction operation, otherwise, directly perform basis reduction operation on basis vectors that meet the reduction conditions;

[0008] The basis vectors that meet the reduction conditions are reduced to the base vectors a1; ...; a i-1 an element in the generated basic domain;

[0009] For the basis vector a j An insertion operation is performed, and a generation matrix and its corresponding Epipodal matrix are updated in real time, and then it is determined whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

[0010] Optionally, determine any Epipodal vector in the Epipodal matrix Is it the shortest non-zero Epipodal vector corresponding to the i-th orthogonal projection, including:

[0011] will be arranged in the original basis vector a i After all subsequent basis vectors have been subjected to the same orthogonal projection in turn, the original basis vectors are compared with their subsequent orthogonal projections in pairs, and the shortest non-zero epipodal vector under each orthogonal projection is found in turn, so that the Hamming weight distribution of each epipodal vector is more balanced.

[0012] Optionally, the step of inputting an arbitrary generator matrix of a binary linear code and calculating an Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix comprises:

[0013] Input a [n,k] binary linear code Any correct generator matrix A is composed of k linearly independent n-dimensional vectors, which are denoted as (a1; ...; a k ), where n and k are the initial parameters of the linear code, respectively, and “means that the Epipodal vectors corresponding to these k basis vectors are all non-zero vectors;

[0014] Calculate the basis vectors (a1; ...; a k ) corresponding to the epipodal vector The epipodal vector corresponding to the basis vector a1 is itself, that is The remaining epipodal vectors can be calculated according to The calculated Epipodal vectors are used as row vectors to form the Epipodal matrix A corresponding to the generated matrix A. + .

[0015] Optionally, determining whether any Epipodal vector in the Epipodal matrix is the shortest non-zero Epipodal vector under the i-th orthogonal projection further includes:

[0016] Initialize the parameter i = 1 and calculate j = i + 1;

[0017] Determine whether the first inequality holds, where π i (·) refers to the operation under the i-th orthogonal projection, |·|, is the bitwise exclusive OR operation between vectors. If the first inequality holds, perform the Lovasz condition judgment on the two basis vectors; otherwise, calculate j = j + 1 and further determine whether the first inequality j < k + 1 holds. If the first inequality holds, further determine whether the first inequality holds; otherwise, calculate i = i + 1, determine whether the first inequality i < k holds. If the first inequality holds, calculate j = i + 1; conversely, output the real-time generator matrix A and its corresponding Epipodal matrix A + ;

[0018] where, i < j < k + 1.

[0019] Optionally, the Lovasz condition judgment on the two basis vectors includes:

[0020] For the two basis vectors a for which the first equation i , a j does not hold, perform the Lovasz condition judgment;

[0021] Determine whether the second inequality holds, where TB(·) is a piecewise function. For TB y (x), if |y| is odd, then TB y (x) = 0; if x j = 0, then TBy(x) = 0, where j = min(Supp(y)), that is, the subscript of the first non-zero element in the vector y; otherwise, TB y (x) = 1 / 2. If the second inequality holds, calculate

[0022] Optionally, the basis reduction operation on the basis vectors that satisfy the reduction condition to reduce them to an element in the fundamental domain generated by (a1; …; a i-1 ) includes:

[0023] Initialize parameter m = max(1, i-1);

[0024] Judge the second inequality Is it true? If the second inequality holds, then calculate Otherwise, m=m-1 is calculated, and when m>0, whether the second inequality holds is determined.

[0025] Optionally, performing an insertion operation on the basis vector includes:

[0026] The basis vector a j Insert into basis vector a i-1 with a i Between, from the basis vector a i To basis vector a j-1 All basis vectors of are shifted one position in turn, that is, (a1; ...; a i-1 ; a i ;…;a j-1 ; a j )=(a1;…;a i-1 ; a j ; a i ;…;a j-1 );

[0027] According to a second aspect, the present invention provides a binary linear code generation matrix reduction device based on a lattice DeepLLL reduction algorithm, the device comprising:

[0028] A first processing module is used for inputting an arbitrary generator matrix of a binary linear code, calculating an Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix;

[0029] A judgment module is used to judge whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection. If not, the two basis vectors are subjected to Lovasz condition judgment. If yes, the generated matrix and its corresponding Epipodal matrix are output; the two basis vectors are subjected to Lovasz condition judgment. If they are satisfied, the basis vectors are subjected to XOR operation, and then the basis vectors that meet the reduction condition are subjected to basis reduction operation. Otherwise, the basis vectors that meet the reduction condition are subjected to basis reduction operation directly; and the basis vectors that meet the reduction condition are subjected to basis reduction operation to be reduced to an element in the generated basic domain;

[0030] The second processing module is used to perform an insertion operation on the basis vectors, and to update the generation matrix and its corresponding Epipodal matrix in real time, and then to determine whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

[0031] Optionally, the judgment module is also used to, after subjecting all basis vectors following the original basis vector to the same orthogonal projection in turn, perform a comparison operation on the original basis vector and the orthogonal projections following it in pairs, and find out in turn the shortest non-zero epipodal vector under each orthogonal projection, so that the Hamming weight distribution of each epipodal vector is more balanced.

[0032] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any one of the above-mentioned binary linear code generation matrix reduction methods based on the lattice DeepLLL reduction algorithm.

[0033] The beneficial effects of the present invention are as follows:

[0034] In the selection operation of whether the Epipodal vector corresponding to any basis vector in a given generator matrix is ​​the shortest non-zero vector under the corresponding orthogonal projection, all basis vectors arranged after the original basis vector are sequentially subjected to the same orthogonal projection and then compared with the basis vectors in pairs, so as to sequentially find the shortest non-zero Epipodal vector under each orthogonal projection, so that the Hamming weight distribution of each Epipodal vector is more balanced; at the same time, further performing a reduction operation on the basis vector that meets the relevant conditions can convert the basis vector into an element in the basic domain generated by a submatrix of the generator matrix, so as to further optimize the Hamming weight of the basis vector; in the operation of inserting the basis vector, for the basis vector that has met the reduction condition, it only needs to be directly inserted into the corresponding order position, rather than exchanging the basis vector before it, so as to improve the efficiency of the calculation in the matrix update stage.

[0035] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented according to the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0037] Figure 1 It is a flow chart of a binary linear code generation matrix reduction method based on a lattice DeepLLL reduction algorithm provided by an embodiment of the present invention;

[0038] Figure 2 It is a structural schematic diagram of a binary linear code generation matrix reduction device based on the lattice DeepLLL reduction algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the present invention.

[0040] There are still many problems in analogizing the reduction algorithm of the related lattice basis to the binary linear code. First of all, the reduction condition in the lattice basis reduction algorithm cannot be directly applied to the setting of the binary linear code. In addition, the reduction in the existing LLL reduction algorithm of the linear code generator matrix is ​​essentially limited to the XOR operation between adjacent basis vectors, so the reduction of each basis vector in the generator matrix is ​​limited. To this end, the present invention extends the reduction condition to each basis vector in the generator matrix and compares it with all the basis vectors after it in turn, and thus proposes a reduction algorithm that analogizes the lattice basis DeepLLL reduction algorithm to the generator matrix on the binary linear code. In other words, the purpose of the present invention is to solve the reduction problem of the generator matrix under the existing binary linear code setting, and provide a binary linear code generator matrix reduction algorithm based on the lattice basis DeepLLL reduction algorithm, so as to achieve the high efficiency of the information set decoding algorithm using the reduced binary linear code generator matrix. The scheme has the characteristics of low storage, high efficiency, high decoding performance, etc. The method of the present invention will be explained and illustrated in detail below:

[0041] The present invention provides a binary linear code generation matrix reduction method based on a lattice DeepLLL reduction algorithm, the method comprising:

[0042] Input an arbitrary generator matrix of a binary linear code, calculate the Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix;

[0043] That is, the embodiment of the present invention is to input a [n, k] binary linear code Any correct generator matrix A is composed of k linearly independent n-dimensional vectors, which are denoted as (a1; ...; a k ), where n and k are the initial parameters of the linear code, "meaning that the epipodal vectors corresponding to the k basis vectors are all non-zero vectors; then the basis vectors (a1; ...; a1) are calculated in sequence k ) corresponding to the epipodal vector The epipodal vector corresponding to the basis vector a1 is itself, that is The remaining epipodal vectors can be calculated according to The calculated Epipodal vectors are used as row vectors to form the Epipodal matrix A corresponding to the generated matrix A. + .

[0044] Determine any Epipodal vector in the Epipodal matrix Is it the shortest non-zero Epipodal vector under the i-th orthogonal projection? If not, it means that there is a basis vector a j , whose length under the i-th orthogonal projection is shorter, the two basis vectors are judged by the Lovasz condition, and if yes, the generated matrix and its corresponding Epipodal matrix are output;

[0045] Specifically, the embodiment of the present invention is to arrange the original basis vector a i After all subsequent basis vectors have been subjected to the same orthogonal projection in turn, the original basis vectors are compared with their subsequent orthogonal projections in pairs, and the shortest non-zero epipodal vector under each orthogonal projection is found in turn, so that the Hamming weight distribution of each epipodal vector is more balanced.

[0046] Perform Lovasz condition judgment on two basis vectors. If they meet the condition, then perform Lovasz condition judgment on basis vector a. j Perform an XOR operation and then enter the basis vector a that satisfies the reduction condition j Perform basis reduction operation, otherwise, directly perform basis reduction operation on basis vectors that meet the reduction conditions;

[0047] The basis vectors that meet the reduction conditions are reduced to the base vectors a1; ...; a i-1 an element in the generated basic domain;

[0048] Specifically, the embodiment of the present invention first initializes the parameter m=max(1,i-1); then determines the second inequality Is it true? If the second inequality holds, then calculate Otherwise, m=m-1 is calculated, and when m>0, whether the second inequality holds is determined.

[0049] For the basis vector a j An insertion operation is performed, and a generation matrix and its corresponding Epipodal matrix are updated in real time, and then it is determined whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

[0050] The embodiment of the present invention performs an insertion operation on the basis vector, including:

[0051] The basis vector a j Insert into basis vector a i-1 with a i Between, from the basis vector a i To basis vector a j-1 All basis vectors of are shifted one position in turn, that is, (a1; ...; a i-1 ; a i ;…;a j-1 ; a j )=(a1;…;a i-1 ; a j ; a i ;…;a j-1 );

[0052] Update the generator matrix A and its corresponding Epipodal matrix A according to the insertion operation + .

[0053] In general, the method described in the embodiment of the present invention is to select whether the Epipodal vector corresponding to any basis vector in a given generator matrix is ​​the shortest non-zero vector under the corresponding orthogonal projection, and then perform a comparison operation in pairs with all basis vectors arranged after the original basis vector, so as to find the shortest non-zero Epipodal vector under each orthogonal projection in turn, so that the Hamming weight distribution of each Epipodal vector is more balanced; at the same time, further performing a reduction operation on the basis vector that meets the relevant conditions can convert the basis vector into an element in the basic domain generated by a submatrix of the generator matrix, thereby further optimizing the Hamming weight of the basis vector; in the operation of inserting the basis vector, for the basis vector that has met the reduction condition, it only needs to be directly inserted into the corresponding order position, instead of exchanging the basis vector before it, thereby improving the efficiency of the calculation in the matrix update stage.

[0054] The following will be combined Figure 1 The method described in the embodiment of the present invention is explained and illustrated in detail by a specific example:

[0055] Step 1. Input the initialization parameters for generation to obtain a specific generation matrix and its Epipodal matrix;

[0056] Step 1.1: Input any "correct" generation matrix A of an [n, k] binary linear code which is composed of k linearly independent n-dimensional vectors, denoted as (a1; …; a k ), in sequence, where n and k are the relevant initial parameters of the linear code, and "correct" means that the Epipodal vectors corresponding to these k basis vectors are all non-zero vectors;

[0057] Step 1.2: Calculate the Epipodal vectors corresponding to the basis vectors (a1; …; a k ) in sequence where the Epipodal vector corresponding to the basis vector a1 is itself, i.e., The remaining Epipodal vectors can be calculated according to and the obtained Epipodal vectors are used as row vectors to form the Epipodal matrix A + corresponding to the generation matrix A.

[0058] Step 2. Judge whether the basis vectors satisfy the reduction condition in sequence. If they do, perform reduction; otherwise, it means that all basis vectors have been reduced, that is, the generation matrix at this time is the "best" generation matrix that can be obtained under the DeepLLL reduction condition, and output the reduced generation matrix;

[0059] Step 2.1: Initialize the parameter i = 1;

[0060] Step 2.2: Calculate j = i + 1;

[0061] Step 2.3: Judge whether the inequality holds, where π i (·) refers to the action under the i-th orthogonal projection, and the specific action expression is |·| specifically uses the definition of Hamming weight, that is, the number of non-zero elements in the vector, and refers to the bitwise exclusive OR operation between vectors. If the inequality holds, perform Step 3; otherwise, perform Step 2.4;

[0062] Step 2.4: Calculate j = j + 1, and judge whether the inequality j < k + 1 holds. If the inequality holds, perform Step 2.3; otherwise, perform Step 2.5;

[0063] Step 2.5: Calculate \(i = i + 1\), and determine whether the inequality \(i < k\) holds. If the inequality holds, proceed to Step 2.2; otherwise, output the real-time generating matrix \(A\) and its corresponding Epipodal matrix \(A\) in the algorithm at this time. + 。

[0064] Step 3, Lovasz condition judgment. The role of this judgment is to perform a preliminary reduction operation on the basis vectors \(a\) that satisfy the inequality condition in Step 2.3, so that the corresponding Epipodal vectors become the non-zero Epipodal vectors with the shortest length under the \(i\)-th orthogonal projection. j 进行初步的约化操作,使其对应的Epipodal向量成为第i个正交投影下长度最短的非零Epipodal向量;

[0065] Step 3.1: For the two basis vectors \(a\) ,a i ,a j that make the inequality

[0066] hold in Step 2.3, perform Lovasz condition judgment. 判断不等式 y (x),若|y|为奇数,则TB y (x)=0;若x j =0,则TB y (x)=0,其中j=min(Supp(y)),即向量y中第一个非零元素的下标;否则,TB y (x)=1 / 2。若不等式成立,则进行步骤3.3;反之,则进行步骤4;

[0067] Step 3.3: Calculate 进行步骤4。

[0068] Step 4: Reduce the basis vectors that satisfy the reduction conditions to the fundamental domain generated by the submatrix composed of the basis vectors \((a_1;\cdots;a\) i-1 )

[0069] Step 4.1: Initialize the parameter \(m=\max(1, i - 1)\);

[0070] Step 4.2: Determine whether the inequality holds, where \(TB(\cdot)\) is the same as \(TB(\cdot)\) in Step 3.2. If the inequality holds, proceed to Step 4.3; otherwise, proceed to Step 4.4;

[0071] Step 4.3: Calculate 进行步骤4.4;

[0072] Step 4.4: Calculate m = m - 1, and determine whether the inequality m > 0 holds. If the inequality holds, proceed to Step 4.2; otherwise, proceed to Step 5.

[0073] Step 5: Perform the insertion operation. The function of this step is to directly insert the basis vector a selected in Step 2.3 into the position of the i-th vector in the generator matrix. This is because the selection condition for a is that the length of its Epipodal vector under the i-th orthogonal projection is shorter. Therefore, after performing the necessary reduction conditions in Steps 3 and 4 above, it is also necessary to adjust its position in the generator matrix. j For a, j the selection condition is that the length of its Epipodal vector under the i-th orthogonal projection is shorter. Therefore, after performing the necessary reduction conditions in Steps 3 and 4 above, it is also necessary to adjust its position in the generator matrix. j After performing the necessary reduction conditions in Steps 3 and 4 above, it is also necessary to adjust its position in the generator matrix.

[0074] Step 5.1: Insert the basis vector a j between the basis vectors a i-1 and a i . Shift all the basis vectors from the basis vector a i to the basis vector a j-1 one position backward in sequence, that is

[0075] (a1; …; a i-1 ; a i ; …; a j-1 ; a j ) = (a1; …; a i-1 ; a j ; a i ; …; a j-1 );

[0076] Step 5.2: Update the generator matrix A and its corresponding Epipodal matrix A + according to the insertion operation in Step 5.1, and proceed to Step 2.

[0077] In comparison, the method described in the embodiment of the present invention is to pairwise compare a i with a during the operation of selecting the shortest non-zero Epipodal vector under the action of each orthogonal projection π i . Among them, i < j < k + 1, that is, all the basis vectors starting from the basis vector a j may be the basis vectors corresponding to the non-zero Epipodal vector with the shortest Hamming weight under the orthogonal projection π i . Such an operation can, to a certain extent, reduce or avoid the occurrence of repeated comparison situations. At the same time, the present invention also performs further reduction operations on the basis vectors that meet the reduction conditions to make them satisfy the fundamental domain generated by the sub-matrix of the corresponding generator matrix, so that the Hamming weight distribution of the corresponding Epipodal vector after reduction is more balanced. i At the same time, the present invention also performs further reduction operations on the basis vectors that meet the reduction conditions to make them satisfy the fundamental domain generated by the sub-matrix of the corresponding generator matrix, so that the Hamming weight distribution of the corresponding Epipodal vector after reduction is more balanced.

[0078] Accordingly, the embodiment of the present invention further provides a binary linear code generation matrix reduction device based on the lattice DeepLLL reduction algorithm, see Figure 2 , the device comprises:

[0079] A first processing module is used for inputting an arbitrary generator matrix of a binary linear code, calculating an Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix;

[0080] A judgment module is used to judge whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection. If not, the two basis vectors are subjected to Lovasz condition judgment. If yes, the generated matrix and its corresponding Epipodal matrix are output; the two basis vectors are subjected to Lovasz condition judgment. If they are satisfied, the basis vectors are subjected to XOR operation, and then the basis vectors that meet the reduction condition are subjected to basis reduction operation. Otherwise, the basis vectors that meet the reduction condition are subjected to basis reduction operation directly; and the basis vectors that meet the reduction condition are subjected to basis reduction operation to be reduced to an element in the generated basic domain;

[0081] The second processing module is used to perform an insertion operation on the basis vectors, and to update the generation matrix and its corresponding Epipodal matrix in real time, and then to determine whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

[0082] In specific implementation, the judgment module described in the embodiment of the present invention is also used to, after performing the same orthogonal projection on all basis vectors arranged after the original basis vector in sequence, perform a comparison operation on the original basis vector and the orthogonal projection after it in groups of two, and find out the shortest non-zero Epipodal vector under each orthogonal projection in sequence, so that the Hamming weight distribution of each Epipodal vector is more balanced.

[0083] In addition, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements any one of the above-mentioned binary linear code generation matrix reduction methods based on the lattice DeepLLL reduction algorithm.

[0084] The relevant contents of the device embodiment and the storage medium embodiment of the present invention can be understood by referring to the method embodiment of the present invention, and will not be discussed in detail here.

[0085] Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, and thus, the scope of the present invention should not be limited to the above embodiments.

Claims

1. A binary linear code generation matrix reduction method based on lattice DeepLLL reduction algorithm, characterized in that: include: Input an arbitrary generator matrix of a binary linear code, calculate the Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix; Determine any Epipodal vector in the Epipodal matrix Is it the shortest non-zero Epipodal vector under the i-th orthogonal projection? If not, it means that there is a basis vector a j , whose length under the i-th orthogonal projection is shorter, and the two basis vectors are judged by the Lovasz condition. If yes, the generated matrix and its corresponding Epipodal matrix are output; Perform Lovasz condition judgment on two basis vectors. If they meet the condition, then perform Lovasz condition judgment on basis vector a. j Perform an XOR operation and then enter the basis vector a that satisfies the reduction condition j Perform a basis reduction operation, otherwise, directly perform a basis reduction operation on the basis vectors that meet the reduction conditions and reduce them to a1; ...; a i-1 an element in the generated basic domain; For the basis vector a j An insertion operation is performed, and a generation matrix and its corresponding Epipodal matrix are updated in real time, and then it is determined whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

2. The method according to claim 1, characterized in that The method of inputting an arbitrary generator matrix of a binary linear code and calculating an Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix comprises: Input a [n,k] binary linear code Any correct generator matrix A is composed of k linearly independent n-dimensional vectors, which are denoted as (a1; ...; a k ), where n and k are the initial parameters of the linear code, respectively, and "means that the Epipodal vectors corresponding to these k basis vectors are all non-zero vectors; Calculate the basis vectors (a1; ...; a k ) corresponding to the epipodal vector The epipodal vector corresponding to the basis vector a1 is itself, that is The remaining epipodal vectors can be calculated according to The calculated Epipodal vectors are used as row vectors to form the Epipodal matrix A corresponding to the generated matrix A. + .

3. The method according to claim 1, characterized in that Determine any Epipodal vector in the Epipodal matrix Is it the shortest non-zero Epipodal vector corresponding to the i-th orthogonal projection, including: will be arranged in the original basis vector a i After all subsequent basis vectors have been subjected to the same orthogonal projection in turn, the original basis vectors are compared with their subsequent orthogonal projections in pairs, and the shortest non-zero epipodal vector under each orthogonal projection is found in turn, so that the Hamming weight distribution of each epipodal vector is more balanced.

4. The method according to claim 3, characterized in that Determining whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection further includes: Initialize parameter i=1, calculate j=i+1; Judge the first inequality to see if it holds, where π i (·) represents the action under the i-th orthogonal projection, |·|, is the bitwise exclusive OR operation between vectors. If the first inequality holds, then perform the Lovasz condition judgment on two basis vectors; otherwise, calculate j = j + 1, and further judge whether the first inequality j < k + 1 holds. If the first inequality holds, then further judge whether the first inequality holds; otherwise, calculate i = i + 1, judge whether the first inequality i < k holds. If the first inequality holds, then calculate j = i + 1; conversely, output the real-time generator matrix A and its corresponding Epipodal matrix A + ; Among them, i <j<k+1。 5. The method according to claim 4, characterized in that The Lovasz conditional judgment on the two basis vectors includes: For the first equation The two basis vectors a i , a j Perform Lovasz conditional judgment; Judge the second inequality Is it true, where TB(·) is a piecewise function, for TB y (x), if |y| is an odd number, then TB y (x) = 0; if x j =0, then TB y (x) = 0, where j = min(Supp(y)), which is the subscript of the first non-zero element in vector y; otherwise, TB y (x) = 1 / 2, if the second inequality holds, then calculate 6. The method according to claim 1, characterized in that The base reduction operation is performed on the basis vectors satisfying the reduction condition, and the basis vectors are reduced to (a1; ...; a i-1 ) is an element in the basic domain generated by: Initialize parameter m = max(1, i-1); Judge the second inequality Is it true? If the second inequality holds, then calculate Otherwise, m=m-1 is calculated, and when m>0, whether the second inequality holds is determined.

7. The method according to claim 1, characterized in that An insertion operation is performed on the basis vector, comprising: The basis vector a j Insert into basis vector a i-1 with a i Between, from the basis vector a i To basis vector a j-1 All basis vectors of are shifted one position in turn, that is, (a1; ...; a i-1 ; a i ;…;a j-1 ; a j )=(a1;…;a i-1 ; a j ; a i ;…;a j-1 ); Update the generator matrix A and its corresponding Epipodal matrix A according to the insertion operation + .

8. A binary linear code generation matrix reduction device based on lattice DeepLLL reduction algorithm, characterized in that: The device comprises: A first processing module is used for inputting an arbitrary generator matrix of a binary linear code, calculating an Epipodal matrix corresponding to the generator matrix and each Epipodal vector in the Epipodal matrix; A judgment module is used to judge whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection. If not, the two basis vectors are subjected to Lovasz condition judgment. If yes, the generated matrix and its corresponding Epipodal matrix are output; the two basis vectors are subjected to Lovasz condition judgment. If they are satisfied, the basis vectors are subjected to XOR operation, and then the basis vectors that meet the reduction condition are subjected to basis reduction operation. Otherwise, the basis vectors that meet the reduction condition are subjected to basis reduction operation directly; and the basis vectors that meet the reduction condition are subjected to basis reduction operation to be reduced to an element in the generated basic domain; The second processing module is used to perform an insertion operation on the basis vectors, and to update the generation matrix and its corresponding Epipodal matrix in real time, and then to determine whether any Epipodal vector in the Epipodal matrix is ​​the shortest non-zero Epipodal vector under the corresponding i-th orthogonal projection.

9. The device according to claim 8, characterized in that The judgment module is also used to, after subjecting all basis vectors arranged after the original basis vector to the same orthogonal projection in sequence, perform a comparison operation on the original basis vector and the orthogonal projections thereafter in pairs, and find out in sequence the shortest non-zero epipodal vector under each orthogonal projection, so that the Hamming weight distribution of each epipodal vector is more balanced.

10. A computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the binary linear code generation matrix reduction method based on the lattice DeepLLL reduction algorithm described in any one of claims 1 to 7 is implemented.

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