Publication: Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound
Authors
Bernal Buitrago, José Joaquín ; Bueno Carreño, Diana H. ; Simón Pinero, Juan Jacobo
item.page.secondaryauthor
item.page.director
Publisher
American Institute of Mathematical Sciences (AIMS)
publication.page.editor
publication.page.department
DOI
https://doi.org/10.3934/amc.2016018
item.page.type
info:eu-repo/semantics/article
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
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.
publication.page.subject
Citation
Advances in Mathematics of Communications, 10 (2), 2016: 459-474
item.page.embargo
Collections
Ir a Estadísticas
Este ítem está sujeto a una licencia Creative Commons. http://creativecommons.org/licenses/by-nc-nd/4.0/