Self-dual codes over a family of local rings
type: Item
instance of: scholarly article
title: Self-dual codes over a family of local rings
zbMATH Open document ID: 1483.94064
author: Steven T. Dougherty
author: Cristina Fernández-Córdoba
author: Roger Ten-Valls
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2021-08-03T00:00:00Z
review text: A \([n,k,d]_q\) code \(C\) is said to be self-dual if it coincides with its orthogonal space, i.e. \(C=C^\perp\). Self-dual codes possess many interesting properties and are closely related to many other mathematical structures. For example, they have connections to groups, designs, lattices and other mathematical objects as well. For this reason, investigation of classes of codes that are self-dual is an important area of study in coding theory. In this paper the authors, generalizing some previous works, construct a family of commutative rings \(R_{q,\Delta}\). After that, they investigate both the structure of these rings and the codes constructed in \(R_{q,\Delta}\). They determine the parameters that provide the existence of self-dual codes exist and give various constructions of them.
reviewed by: Matteo Bonini
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7377724
zbMATH Keywords: self-dual codes
zbMATH Keywords: codes over rings
zbMATH Keywords: local rings
MaRDI profile type: Publication
full work available at URL: s00200-020-00466-4
OpenAlex ID: W3092313103
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DOI: 10.1007/S00200-020-00466-4
description: scientific article; zbMATH DE number 7377724