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arXiv · 2402.03965

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

José Joaquín Bernal·Diana H. Bueno-Carreño·Juan Jacobo Simón
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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.

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José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón. 2024-02-06. Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound. https://arxiv.org/abs/2402.03965

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