On Quasi-Cyclic Codes as a Generalization of Cyclic Codes

Abstract : 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.
Type de document :
Article dans une revue
Finite Fields and Their Applications, Elsevier, 2012, 18 (5), pp.904-919. 〈10.1016/j.ffa.2012.06.003〉
Liste complète des métadonnées

https://hal.inria.fr/inria-00615276
Contributeur : Morgan Barbier <>
Soumis le : vendredi 25 mai 2012 - 13:27:20
Dernière modification le : jeudi 10 mai 2018 - 02:06:16
Document(s) archivé(s) le : dimanche 26 août 2012 - 02:36:49

Fichiers

article.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Morgan Barbier, Christophe Chabot, Guillaume Quintin. On Quasi-Cyclic Codes as a Generalization of Cyclic Codes. Finite Fields and Their Applications, Elsevier, 2012, 18 (5), pp.904-919. 〈10.1016/j.ffa.2012.06.003〉. 〈inria-00615276v2〉

Partager

Métriques

Consultations de la notice

624

Téléchargements de fichiers

258