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A class of primitive BCH codes and their weight distribution

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. Recently, several classes of BCH codes with length \(n=q^m-1\) and designed distances \(\delta =(q-1)q^{m-1}-1-q^{\lfloor (m-1)/2\rfloor }\) and \(\delta =(q-1)q^{m-1}-1-q^{\lfloor (m+1)/2\rfloor }\) were widely studied, where \(m\ge 4\) is an integer. In this paper, we consider the case \(m=3\). The weight distribution of a class of primitive BCH codes with designed distance \(q^3-q^2-q-2\) is determined, which solves an open problem put forward in Ding et al. (Finite Fields Appl 45:237–263, 2017).

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Acknowledgements

The authors are grateful to the anonymous reviewers for their careful reading of the original version of this paper, their detailed comments and suggestions, which have much improved the quality of this paper.

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  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Haode Yan

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  1. Haode Yan
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Yan, H. A class of primitive BCH codes and their weight distribution. AAECC 29, 1–11 (2018). https://doi.org/10.1007/s00200-017-0320-4

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  • DOI: https://doi.org/10.1007/s00200-017-0320-4

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