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

José Joaquín Bernal | Zendy; Diana H. Bueno-Carreño | Zendy; Juan Jacobo Simón | Zendy

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

Author(s) -

José Joaquín Bernal,

Diana H. Bueno-Carreño,

Juan Jacobo Simón

Publication year - 2016

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2016018

Subject(s) - bch code , mathematics , minimum distance , abelian group , polynomial code , polynomial , discrete mathematics , combinatorics , reed–solomon error correction , binary code , binary number , linear code , block code , algorithm , error detection and correction , arithmetic , decoding methods , mathematical analysis

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.

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