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Designs, Codes and Cryptography

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31-07-2018

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

Authors: Selçuk Kavut, Seher Tutdere

Published in: Designs, Codes and Cryptography | Issue 2-3/2019

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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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Title: The covering radii of a class of binary cyclic codes and some BCH codes
Authors: Selçuk Kavut
Seher Tutdere
Publication date: 31-07-2018
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 2-3/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0525-y

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