Minimal cyclic codes of length \(p^{n} q\).
type: Item
instance of: scholarly article
title: Minimal cyclic codes of length \(p^{n} q\).
zbMATH Open document ID: 1038.94013
DOI: 10.1016/S1071-5797(03)00023-6
author: Gurmeet K. Bakshi
author: Madhu Raka
published in: Finite Fields and their Applications
publication date: 2003-11-19T00:00:00Z
review text: Explicit expressions for all the \(3n+2\) primitive idempotents in the ring \(R_{p^nq}= \text{GF} (l)[x]/(x^{p^nq}-1)\), where \(p\), \(q\), \(l\) are distinct odd primes satisfying some conditions, are derived. The dimension, generating polynomials and minimum distance of the minimal cyclic codes of length \(p^nq\) are also discussed. As an example, all the ternary minimal cyclic codes of length 35 are described. See also the corrigendum [ibid. 18, No. 4, 863 (2012; Zbl 1247.94048)].
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T30
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 2005892
zbMATH Keywords: cyclic codes
zbMATH Keywords: primitive idempotents
zbMATH Keywords: generating polynomials
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005892