Quasi-cyclic codes as codes over rings of matrices
type: Item
instance of: scholarly article
title: Quasi-cyclic codes as codes over rings of matrices
zbMATH Open document ID: 1193.94072
author: Pierre-Louis Cayrel
author: Christophe Chabot
author: Abdelkader Necer
published in: Finite Fields and their Applications
publication date: 2010-04-15T00:00:00Z
review text: This paper considers quasi-cyclic codes as cyclic codes over a ring of matrices over \(\mathbb{F}_q\). One of the main results of this paper is to generalize the correspondence between linear recurring sequences over a finite field and cyclic codes to the case of linear recurring sequences over a ring of matrices. The existence of the exponent for a polynomial with matricial coefficients has been shown. The construction of new quasi-cyclic codes and self-dual Euclidean codes (and Hermitian over \(\mathbb{F}_4\)) has also been taken up. Such a construction permits to find new self-dual Euclidean codes with parameters \([28,14,9]\) over \(\mathbb{F}_4\).
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 5693359
zbMATH Keywords: quasi-cyclic codes
zbMATH Keywords: linear recurrent sequences
zbMATH Keywords: rings of matrices
zbMATH Keywords: self-dual codes
MaRDI profile type: Publication
full work available at URL: j.ffa.2010.01.001
OpenAlex ID: W1987011728
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DOI: 10.1016/J.FFA.2010.01.001
description: scientific article; zbMATH DE number 5693359