Quasi-Cyclic Codes from Cyclic-Structured Designs with Good Properties

Design of LDPC Codes: A Survey and New Results

This survey paper provides fundamentals in the design of LDPC codes. To provide a target for the code designer, we first summarize the EXIT chart technique for determining (near-)optimal degree distributions for LDPC code ensembles. We also demonstrate the simplicity of representing codes by protographs and how this naturally leads to quasi-cyclic LDPC codes. The EXIT chart technique is then ex...

Good Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes

As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...

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

New Good Quasi-cyclic Codes over Gf(3)

Abstract In this paper some good quasi-cyclic codes over GF(3) are presented. These quasi-cyclic codes improve the already known lower bounds on the minimum distance of the previously known quasi-cyclic codes. Even though these codes do not improve the minimum distance of the best unstructured code known, their beautiful structure and simplicity provide several advantages in comparison to other...

On quasi-cyclic codes as a generalization of cyclic codes

In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length lm and ideals of Ml(Fq)[X]/(X m −1). This permits to construct new classes of codes, namely quasi-BCH and quasi-evaluation codes. We study th...