On the cyclic order distribution and partitioning of linear cyclic codes
type: Item
instance of: scholarly article
title: On the cyclic order distribution and partitioning of linear cyclic codes
zbMATH Open document ID: 1481.94154
author: Gustavo Terra Bastos
author: José Sampaio de Lemos-Neto
published in: São Paulo Journal of Mathematical Sciences
publication date: 2021-07-28T00:00:00Z
review text: In this paper, the authors present a method to directly compute the number of codewords of \(C\) with cyclic order \(i\), for \(1\leq i\leq n\) and \(i|n\), and consequently the number of cyclic equivalence classes of \(C\) (practically, it is a way to partition any linear cyclic code in its cyclic equivalence classes according to the algebraic structure of the code). Such partition is useful to generate cyclically permutable codes directly from linear cyclic codes. Moreover, the authors prove a theorem to directly obtain the leaders of the cyclic equivalence classes of a linear cyclic code \(C\) (no other constraints except the size of the finite field and the block length of the code must be coprimes). Finally, they present a criterion to construct maximal cyclic order codes.
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7375695
zbMATH Keywords: cyclically permutable codes
zbMATH Keywords: linear cyclic codes
zbMATH Keywords: cyclic equivalence classes
zbMATH Keywords: \(x\)-cyclotomic cosets
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: s40863-020-00197-x
OpenAlex ID: W3097204850
Wikidata QID: Q107169731
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DOI: 10.1007/S40863-020-00197-X
description: scientific article; zbMATH DE number 7375695