Duadic \(\mathbb{Z}_4\)-codes
type: Item
instance of: scholarly article
title: Duadic \(\mathbb{Z}_4\)-codes
zbMATH Open document ID: 1017.94030
author: Philippe Langevin
author: Patrick Solé
published in: Finite Fields and their Applications
publication date: 2000-12-19T00:00:00Z
review text: The structure of abelian \(\mathbb{Z}_4\)-codes (and more generally \(\mathbb{Z}_{p^n}\)-codes) is studied. A criterion for self-duality is derived. An arithmetic test on the length for the existence of nontrivial abelian self-dual codes is derived. A natural generalization of both the supplemented quadratic residue codes and the binary duadic codes is introduced. Isodual abelian \(\mathbb{Z}_4\)-codes are considered and used to produce \(4\)-modular lattices. Some results of this paper were generalized later by \textit{S. Ling} and \textit{P. Solé} [Appl. Algebra Eng. Commun. Comput. 12, 365-379 (2001; Zbl 1030.94041)].
reviewed by: Carlos Munuera
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 1545693
zbMATH Keywords: modular lattices
zbMATH Keywords: abelian self-dual codes
zbMATH Keywords: quadratic residue codes
zbMATH Keywords: duadic codes
MaRDI profile type: Publication
full work available at URL: ffta.2000.0285
OpenAlex ID: W1997847814
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DOI: 10.1006/FFTA.2000.0285
description: scientific article; zbMATH DE number 1545693