List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes

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

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

Practical Encoder and Decoder for Power Constrained QC-LDPC lattices

LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as a special case of LDPC lattices with one binary QC-LDPC code as their underlying code. These lattices are obtained from Construction A of lattices providing ...

Quasi-cyclic LDPC codes from difference families

We consider in this paper regular and nearly regular quasi-cyclic low-density paritycheck (LDPC) codes, derived from families of difference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding.

Codes Closed under Arbitrary Abelian Group of Permutations

Algebraic structure of codes over Fq , closed under arbitrary abelian group G of permutations with exponent relatively prime to q, called G-invariant codes, is investigated using a transform domain approach. In particular, this general approach unveils algebraic structure of quasicyclic codes, abelian codes, cyclic codes, and quasi-abelian codes with restriction on G to appropriate special case...