\(\mathbb{Z}_{p}\mathbb{Z}_{p}[u]\)-additive cyclic codes
type: Item
instance of: scholarly article
title: \(\mathbb{Z}_{p}\mathbb{Z}_{p}[u]\)-additive cyclic codes
zbMATH Open document ID: 1431.94183
DOI: 10.1504/IJICOT.2018.091815
author: Lingyu Diao
author: Jian Gao
published in: International Journal of Information and Coding Theory
publication date: 2018-11-05T00:00:00Z
review text: Summary: Additive cyclic codes of length \((\alpha,\beta)\) over \(\mathbb Z_p\mathbb Z_p[u]\) can be viewed as \(\mathbb Z_p[u][x]\)-submodules of \(\mathbb Z_p[x]/(x^\alpha - 1) \times \mathbb Z_p[u][x]/(x^\beta - 1)\), where \(\mathbb Z_p[u] = \mathbb Z_p + u\mathbb Z_p\), \(u^2 = 0\). In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as \(\mathbb Z_p[u]\)-submodules of \(\mathbb Z_p[x] / (x^\alpha-1) \times \mathbb Z_p[u][x] / (x^\beta-1)\). Further, we also determine the generator polynomials of the dual codes of \(\mathbb Z_p\mathbb Z_p[u]\)-additive cyclic codes. Moreover, some binary quantum codes are constructed by additive cyclic codes over \(\mathbb Z_2\mathbb Z_2[u]\).
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 81P70
zbMATH DE Number: 6973112
zbMATH Keywords: additive cyclic codes
zbMATH Keywords: minimal generating sets
zbMATH Keywords: binary quantum codes
MaRDI profile type: Publication
full work available at URL: ijicot.2018.091815
OpenAlex ID: W4254882066
description: scientific article; zbMATH DE number 6973112