Half-cyclic, dihedral and half-dihedral codes
type: Item
instance of: scholarly article
title: Half-cyclic, dihedral and half-dihedral codes
zbMATH Open document ID: 1492.94203
author: Primož Potočnik
author: Robert Jajcay
author: Steve Wilson
published in: Journal of Applied Mathematics and Computing
publication date: 2021-11-29T00:00:00Z
review text: Motivated by the study of a family of graphs introduced by \textit{C. E. Praeger} and \textit{M. Xu} [Eur. J. Comb. 10, No. 1, 91--102 (1989; Zbl 0672.05040)], the authors of the paper under review study linear codes in \(\mathbb{F}_2^n\) which are invariant under the actions of some subgroups of the dihedral group \(\mathbb{D}_n=\langle R,M\rangle\), where \(R\) is a cyclic rotation of the positions of the code and \(M\) reverses the codewords. So, they introduce the following terminologies: a code in \(\mathbb{F}_2^n\) is said half-cyclic/dihedral/half-dihedral if it is invariant under the action of \(\langle R^2\rangle\) / \(\langle R,M\rangle\) / \(\langle R^2,M\rangle\), respectively. In Theorem 2.11, the authors classify half-cyclic codes, in Theorem 3.3 they classify the dihedral codes and in Theorem 3.5 classify half-dihedral codes.
reviewed by: Ferdinando Zullo
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 7435154
zbMATH Keywords: linear codes
zbMATH Keywords: cyclic codes
zbMATH Keywords: half-cyclic codes
zbMATH Keywords: code symmetries
MaRDI profile type: Publication
full work available at URL: s12190-020-01374-z
OpenAlex ID: W3036646213
cites work: New binary linear codes from quasi-cyclic codes and an augmentation algorithm
cites work: On quasi-cyclic codes as a generalization of cyclic codes
cites work: Quasi-cyclic codes as codes over rings of matrices
cites work: Q4726166
cites work: Q5234635
cites work: On the algebraic structure of quasi-cyclic codes .I. Finite fields
cites work: On the algebraic structure of quasi-cyclic codes. II: Chain rings
cites work: On the Algebraic Structure of Quasi-Cyclic Codes III: Generator Theory
cites work: On the algebraic structure of quasi-cyclic codes. IV: Repeated roots
cites work: Quasi-twisted codes with constacyclic constituent codes
DOI: 10.1007/S12190-020-01374-Z
Recommended article: Q3496285
Recommended article: Q4694262
Recommended article: Self-dual 2-quasi-cyclic codes and dihedral codes
Recommended article: Cocyclic Hadamard codes
Recommended article: Q3737370
Recommended article: Q3552578
Recommended article: Hulls of double cyclic codes
Recommended article: Quasi-Cyclic Codes
Recommended article: On cyclic self-dual codes
Recommended article: A class of generalized cyclic codes
description: scientific article; zbMATH DE number 7435154