Additive and linear conjucyclic codes over \(\mathbb{F}_4\)
type: Item
instance of: scholarly article
title: Additive and linear conjucyclic codes over \(\mathbb{F}_4\)
zbMATH Open document ID: 1491.94084
author: Taher Abualrub
author: Steven T. Dougherty
published in: Advances in Mathematics of Communications
publication date: 2022-01-24T00:00:00Z
review text: In this paper, the authors are interested in linear and additive conjucyclic codes over the finite field \(\mathbb{F}_4\). There is produced a special kind of duality for which the orthogonal (with respect to that duality) of conjucyclic codes is conjucyclic. Moreover, there is shown that this is not the case for other standard dualities. The authors prove that additive conjucyclic codes are the only non-trivial conjucyclic codes over \(\mathbb{F}_4\) and they classify these codes by linear algebraic approach. Finally, there is shown that additive conjucyclic codes of length \(n\) over \(\mathbb{F}_4\) are isomorphic to binary cyclic codes of length \(2n\).
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7461984
zbMATH Keywords: conjucyclic code
zbMATH Keywords: additive code
zbMATH Keywords: codes over \(\mathbb{F}_4\)
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: amc.2020096
OpenAlex ID: W3045839094
cites work: Quantum error correction via codes over GF(4)
cites work: Algebraic Coding Theory Over Finite Commutative Rings
cites work: Q4578229
cites work: Orthogonality from group characters
cites work: Q3884021
cites work: Secret sharing schemes based on additive codes over \(\mathrm{GF}(4)\)
cites work: Constacyclic codes as invariant subspaces
DOI: 10.3934/AMC.2020096
description: scientific article; zbMATH DE number 7461984