Cyclic and BCH codes whose minimum distance equals their maximum BCH bound

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2016Embargo end date: 01 Jan 2024Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Advances in Mathematics of Communications, volume 10, pages 459-474 (issn: 1930-5346, eissn: 1930-5338,

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Authors: José Joaquín Bernal; Diana H. Bueno-Carreño; Juan Jacobo Simón;

doi: 10.3934/amc.2016018 , 10.48550/arxiv.2402.03965

arXiv: 2402.03965

Cyclic and BCH codes whose minimum distance equals their maximum BCH bound

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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 delta, that have minimum distance d(C)= delta. 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.

Related Organizations

Pontificia Universidad Javeriana
Colombia
University of Murcia
Spain

Keywords

FOS: Computer and information sciences, cyclic codes, Computer Science - Information Theory, Information Theory (cs.IT), BCH bound, BCH codes, Bounds on codes, apparent distance, minimum distance, Cyclic codes

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