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Pré-Publication, Document De Travail Année : 2011

On Quasi-Cyclic Codes as a Generalization of Cyclic Codes

Résumé

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 m and ideals of M_l(Fq )[X]/(X^m −1). This permits to construct new classes of codes, namely quasi-BCH and quasi-evaluation codes. We study the parameters of such codes and propose a decoding algorithm up to half the designed minimum distance. We even found one new quasi-cyclic code with better parameters than known [189, 11, 125]_F4 and 48 derivated codes beating the known bounds as well.
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Dates et versions

inria-00615276 , version 1 (18-08-2011)
inria-00615276 , version 2 (25-05-2012)

Identifiants

  • HAL Id : inria-00615276 , version 1
  • ARXIV : 1108.3754

Citer

Morgan Barbier, Christophe Chabot, Guillaume Quintin. On Quasi-Cyclic Codes as a Generalization of Cyclic Codes. 2011. ⟨inria-00615276v1⟩
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