Computation of Grobner Basis for Systematic Encoding of Generalized Quasi-Cyclic Codes

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Computation of Minimum Hamming Weight for Linear Codes

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes

Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Griihner bases for modules gives a compact description and implementation of a systematic encoder. We present examples of algebraic-geometric Goppa codes that can be encoded by these methods, including the one-point Hermitian codes. Index TermsSystematic encoding, algebraic-geometr...

Nonbinary Quasi-Cyclic LDPC Cycle Codes with Low-Density Systematic Quasi-Cyclic Generator Matrices

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...

Quasi-cyclic self-dual codes of length 70

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant