On Quasi-Cyclic Codes as a Generalization of Cyclic CodesReportar como inadecuado




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* Corresponding author 1 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau 2 GRACE - Geometry, arithmetic, algorithms, codes and encryption Inria Saclay - Ile de France 3 CASYS - Calculs Algébriques et Systèmes Dynamiques LJK - Laboratoire Jean Kuntzmann

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 lFq 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.

Keywords : key equation decoding algorithm principal ideals Quasi-cyclic codes





Autor: Morgan Barbier - Christophe Chabot - Guillaume Quintin -

Fuente: https://hal.archives-ouvertes.fr/



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