The H-matrix in Eq. (6.52) is known as the parity-check matrix. We can easily verify that: (6.53)GHT=[IkP][PIn−k]=P+P=0, meaning that the parity-check matrix of an (n,k) linear block code H is a matrix of rank n − k and dimensions (n − k)× n whose null space...
An identification scheme based on parity check matrix of error-correcting codes over GF(2) was proposed in the paper "A New Paradigm for Public Key Identification" by J. Stern(1996), a new identification scheme based on parity check matrix of rank distance codes over GF(qN) (q is a prim...
2.The generator matrix andcheck matrixof q-cyclic codes are discussed,and then the theory of rank distance codes can be studied expediently.讨论了q-循环码的生成矩阵和校验矩阵,从而可以方便地研究秩距离码的理论。 3.Although thecheck matrixof LDPC codes is sparse,the generator matrix is not.LDPC...
The present invention, a determining unit for determining whether a parity check matrix received from the outside has a maximum rank (rank); In response to the determination result of the determining unit, rows or columns that are linearly dependent on each other among the rows or columns of ...
Noun1.parity check- a system of checking for errors in computer functioning odd-even check,redundancy check confirmation,substantiation,verification,check- additional proof that something that was believed (some fact or hypothesis or theory) is correct; "fossils provided further confirmation of the evol...
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed in...
The generator matrix and check matrix of q-cyclic codes are discussed,and then the theory of rank distance codes can be studied expediently. 讨论了q-循环码的生成矩阵和校验矩阵,从而可以方便地研究秩距离码的理论。 3. Although the check matrix of LDPC codes is sparse,the generator matrix is no...
Abstract Weaknesses of Margulis and Ramanujan–Margulis Low-Density Parity-Check Codes
From the random matrix theory point of view we obtain results on the rank distribution of column submatrices. We give... AA Klyachko,Ibrahim OEzen - 《Finite Fields & Their Applications》 被引量: 11发表: 2009年 The Triple-Parity Law Scientists and epistemologists agree that a scientific law...
(3.25) is proportional to the photino mass parameter, mγ˜ = M1c2W + M2s2W , and that the exact determinant of the generalized neutralino mass matrix in eq. (2.13) (after restricting to the nontrivial rank-5 subspace and for ηα = 0) is still proportional to mγ˜. Though m...