\(\mathbb Z_2\mathbb Z_4\)-linear codes: Generator matrices and duality
type: Item
instance of: scholarly article
title: \(\mathbb Z_2\mathbb Z_4\)-linear codes: Generator matrices and duality
zbMATH Open document ID: 1185.94092
published in: Designs, Codes and Cryptography
publication date: 2010-02-25T00:00:00Z
review text: This paper develops a general theory for \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes including generator matrices, parity-check matrices and duality. Such class of codes includes binary and quaternary linear codes generalizing them. There are some interesting classes of nonlinear binary codes that can be viewed as \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes but not as \(\mathbb{Z}_4\)-linear codes. Moreover, \(\mathbb{Z}_2\mathbb{Z}_4\) duality shows that \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes cannot be considered only as a variant of \(\mathbb{Z}_4\)-linear codes.
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 5675131
zbMATH Keywords: binary linear codes
zbMATH Keywords: quaternary linear codes
zbMATH Keywords: \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes
zbMATH Keywords: \(\mathbb{Z}_2\mathbb{Z}_4\)-additive codes
author: J. Borges
author: Cristina Fernández-Córdoba
author: J. Pujol
author: Josep Rifà
author: M. Villanueva
reviewed by: Bai Kishan Dass
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: s10623-009-9316-9
OpenAlex ID: W2010238614
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DOI: 10.1007/S10623-009-9316-9
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description: scientific article; zbMATH DE number 5675131