A study of cyclic and constacyclic codes over \(\mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\)
type: Item
instance of: scholarly article
title: A study of cyclic and constacyclic codes over \(\mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\)
zbMATH Open document ID: 1431.94186
DOI: 10.1504/IJICOT.2018.095017
author: Habibul Islam
author: Om Prakash
published in: International Journal of Information and Coding Theory
publication date: 2018-11-05T00:00:00Z
review text: Summary: In this paper, we study some properties of cyclic and constacyclic codes over the ring \(R = \mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\) where \(u^{2} = v^2 = uv = vu = 0\). The generator polynomials and minimal spanning set for cyclic codes over \(R\) are determined. Further, \((1 + 2u)\)-constacyclic codes are considered and find the cyclic, quasi-cyclic and permutation equivalent to a QC code over \(\mathbb Z_{4}\) as the Gray images of \((1 + 2u)\)-constacyclic codes over \(R\).
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 6973121
zbMATH Keywords: cyclic code
zbMATH Keywords: minimal spanning set
zbMATH Keywords: constacyclic code
zbMATH Keywords: quasi-cyclic code
zbMATH Keywords: Gray map
MaRDI profile type: Publication
full work available at URL: ijicot.2018.095017
OpenAlex ID: W4252716299
description: scientific article; zbMATH DE number 6973121