\(\mathbb F_q\)-linear cyclic codes over \(\mathbb F_{q^m}\): DFT approach
type: Item
instance of: scholarly article
title: \(\mathbb F_q\)-linear cyclic codes over \(\mathbb F_{q^m}\): DFT approach
zbMATH Open document ID: 1070.94028
author: Bikash Kumar Dey
author: B. Sundar Rajan
published in: Designs, Codes and Cryptography
publication date: 2005-02-28T00:00:00Z
review text: Codes over \(\mathbb F_{q^m}\) that are closed under addition and multiplication with elements from \(\mathbb F_q\) are called \(\mathbb F_q\)-linear codes over \(\mathbb F_{q^m}\). A transform domain characterization is obtained of \(\mathbb F_q\)-linear cyclic codes using the discrete Fourier transform over an extension field of \(\mathbb F_{q^m}\). A transform domain condition is given for two vectors to be \(\mathbb F_q\)-dual of each other. This is used to prove the nonexistence of certain self-dual \(\mathbb F_q\)-linear cyclic codes and equivalently the nonexistence of the corresponding self-dual quasi-cyclic codes. The transform domain characterization of \(\mathbb F_q\)-linear cyclic codes is used to derive minimum distance bound for the corresponding quasi-cyclic codes.
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 2139211
zbMATH Keywords: cyclic codes
zbMATH Keywords: discrete Fourier Transform
zbMATH Keywords: transform domain
zbMATH Keywords: self-dual codes
zbMATH Keywords: quasi-cyclic codes
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
full work available at URL: s10623-003-4196-x
OpenAlex ID: W2075451506
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DOI: 10.1007/S10623-003-4196-X
description: scientific article; zbMATH DE number 2139211