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The covering radii of a class of binary cyclic codes and some BCH codes

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Abstract

In 2003, Moreno and Castro proved that the covering radius of a class of primitive cyclic codes over the finite field \(\mathbb {F}_2\) having minimum distance 5 (resp. 7) is 3 (resp. 5). We here give a generalization of this result as follows: the covering radius of a class of primitive cyclic codes over \(\mathbb {F}_2\) with minimum distance greater than or equal to \(r+2\) is r, where r is any odd integer. Moreover, we prove that the primitive binary e-error correcting BCH codes of length \(2^f-1\) have covering radii \(2e-1\) for an improved lower bound of f.

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Acknowledgements

This work is supported by the Project of Scientific Investigation (BAP 2015-A17), Gebze Technical University, Turkey.

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Authors and Affiliations

  1. Department of Computer Engineering, Balıkesir University, Balıkesir, Turkey

    Selçuk Kavut

  2. Department of Mathematics, Gebze Technical University, Gebze, Kocaeli, Turkey

    Seher Tutdere

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  1. Selçuk Kavut
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  2. Seher Tutdere
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Correspondence to Seher Tutdere.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

This is a revised and extended version of the extended abstract “The covering radii of a class of binary cyclic codes and some BCH codes” presented in the “Tenth International Workshop on Coding and Cryptography (WCC 2017)”, September 18–22, 2017, Saint-Petersburg, Russia. Section 3 of this paper contains new material over the workshop version.

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Kavut, S., Tutdere, S. The covering radii of a class of binary cyclic codes and some BCH codes. Des. Codes Cryptogr. 87, 317–325 (2019). https://doi.org/10.1007/s10623-018-0525-y

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  • DOI: https://doi.org/10.1007/s10623-018-0525-y

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