Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound

Bernal Buitrago, José Joaquín; Bueno Carreño, Diana H.; Simón Pinero, Juan Jacobo

Publication:
Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound

dc.contributor.author	Bernal Buitrago, José Joaquín
dc.contributor.author	Bueno Carreño, Diana H.
dc.contributor.author	Simón Pinero, Juan Jacobo
dc.contributor.department	Matemáticas
dc.date.accessioned	2024-02-07T09:12:30Z
dc.date.available	2024-02-07T09:12:30Z
dc.date.issued	2016
dc.description	©2016. This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted, version of a Published Work that appeared in final form in Advances in Mathematics of Communications (AMC). To access the final edited and published work see https://doi.org/10.3934/amc.2016018
dc.description.abstract	In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form X^n −1. We apply our results to the study of those BCH codes C, with designed distance δ, that have minimum distance d(C) = δ. Finally, we present some examples of new binary BCH codes satisfying that condition. To do this, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes.	es
dc.format	application/pdf	es
dc.format.extent	11	es
dc.identifier.citation	Advances in Mathematics of Communications, 10 (2), 2016: 459-474
dc.identifier.doi	https://doi.org/10.3934/amc.2016018
dc.identifier.uri	http://hdl.handle.net/10201/138834
dc.language	eng	es
dc.publisher	American Institute of Mathematical Sciences (AIMS)	es
dc.relation	MINECO (Ministerio de Economía y Competitividad), (Fondo Europeo de Desarrollo Regional) project MTM2012-35240, Programa Hispano Brasileño de Cooperación Universitaria PHB2012-0135, and Fundación Séneca of Murcia. Departamento Administrativo de Ciencia, Tecnología e Innovación de la República de Colombia.	es
dc.rights	info:eu-repo/semantics/openAccess	es
dc.rights	Attribution-NoCommercial-NoDerivatives 4.0 Internacional	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.title	Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es