A class of constacyclic codes over \(\mathbb Z_{p^m}\)
type: Item
instance of: scholarly article
title: A class of constacyclic codes over \(\mathbb Z_{p^m}\)
zbMATH Open document ID: 1201.94123
author: Shixin Zhu
author: Xiaoshan Kai
published in: Finite Fields and their Applications
publication date: 2010-07-07T00:00:00Z
review text: This paper presents the structure of \((1+\lambda p)\)-constacyclic codes of length \(p^s\) over \(\mathrm{GR}(p^m,a)\) and determine the Hamming and homogeneous distances of all such constacyclic codes. Further, the authors have classified all \((1+\lambda p)\)-constacyclic codes over \(\mathbb Z_{p^m}\) of length \(N= p^sn\) (\(n\) prime to \(p\)) using the discrete Fourier transform. The last section deals with \((1+\lambda p)\)-constacyclic codes over \(\mathbb Z_{p^2}\) and their images under a generalization of the Gray map.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 5731594
zbMATH Keywords: constacyclic codes
zbMATH Keywords: Galois rings
zbMATH Keywords: generator polynomials
zbMATH Keywords: discrete Fourier transform
MaRDI profile type: Publication
full work available at URL: j.ffa.2010.03.003
OpenAlex ID: W2058437000
cites work: Cyclic codes over \(\mathbb{Z}_{4}\) of oddly even length.
cites work: Negacyclic codes over Z/sub 4/ of even length
cites work: Negacyclic Codes of Length&lt;tex&gt;$2^s$&lt;/tex&gt;Over Galois Rings
cites work: Complete Distances of All Negacyclic Codes of Length $2^{s}$ Over $\BBZ _{2^{a}}$
cites work: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions
cites work: Cyclic and Negacyclic Codes Over Finite Chain Rings
cites work: Cyclic codes over \(\mathbb Z_4\) of even length
cites work: On modular cyclic codes
cites work: Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code
cites work: The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
cites work: Z(p/sup k+1/)-linear codes
cites work: Q4046212
cites work: Repeated-root cyclic and negacyclic codes over a finite chain ring
cites work: A generalization of negacyclic codes
cites work: Some constacyclic codes over \({\mathbb Z}_{2^k}\) and binary quasi-cyclic codes.
cites work: Negacyclic and cyclic codes over Z/sub 4/
cites work: Binary images of cyclic codes over Z/sub 4/
cites work: The Hamming distances of negacyclic codes of length \(2^s\) over \(GR (2^a , m )\)
cites work: Dual and self-dual negacyclic codes of even length over \(\mathbb Z_{2^a}\)
DOI: 10.1016/J.FFA.2010.03.003
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description: scientific article; zbMATH DE number 5731594