On the distances of cyclic codes of length \(2^e\) over \(\mathbb Z_4\)
type: Item
instance of: scholarly article
title: On the distances of cyclic codes of length \(2^e\) over \(\mathbb Z_4\)
zbMATH Open document ID: 1182.94058
author: Xiaoshan Kai
author: Shixin Zhu
published in: Discrete Mathematics
publication date: 2009-12-15T00:00:00Z
review text: Cyclic codes of length \(2^e\) over \(\mathbb{Z}_4\) are precisely the ideals of the local ring \(\mathbb{Z}_4[X]/(X^{2^e}-1)\); their structure was determined by \textit{T. Abualrub} and \textit{R. Oehmke} (see for instance [Discrete Appl. Math. 128, No. 1, 3--9 (2003; Zbl 1025.94022)] or the article by \textit{S. Dougherty} and \textit{S. Ling} [Des. Codes Cryptography 39, No. 2, 127--153 (2006; Zbl 1172.94637)]). Using these results, the authors investigate the Hamming and the Lee distances of such codes; they give a complete list of the distances with exact results in nearly all 23 cases; exceptions are the Lee distances of three cases for which upper and lower bounds are given.
reviewed by: Ralph-Hardo Schulz
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 5648167
zbMATH Keywords: cyclic codes
zbMATH Keywords: quaterny codes
zbMATH Keywords: Hamming distances
zbMATH Keywords: Lee distances
zbMATH Keywords: codes over rings
MaRDI profile type: Publication
full work available at URL: j.disc.2009.07.018
OpenAlex ID: W1983483270
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DOI: 10.1016/J.DISC.2009.07.018
description: scientific article; zbMATH DE number 5648167