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A non-cyclic triple-error-correcting BCH-like code and some minimum distance results

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Abstract

In this paper, we give the first example of a non-cyclic triple-error-correcting code which is not equivalent to the primitive BCH code. It has parameters [63, 45, 7]. We also give better bounds on minimum distances of some [2n − 1, 2n - 3n - 1] cyclic codes with three small zeroes. Finally, we reprove weight distribution results of Kasami for triple-error-correcting BCH-like codes using direct methods.

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Authors and Affiliations

  1. Department of Mathematics, School of Physical & Mathematical Sciences, Nanyang Technology University, Singapore, Singapore

    Carl Bracken

  2. School of Mathematical Sciences, University College Dublin, Dublin, Ireland

    Faruk Göloğlu

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  1. Carl Bracken
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  2. Faruk Göloğlu
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Correspondence to Faruk Göloğlu.

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Communicated by J. D. Key.

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Bracken, C., Göloğlu, F. A non-cyclic triple-error-correcting BCH-like code and some minimum distance results. Des. Codes Cryptogr. 72, 317–330 (2014). https://doi.org/10.1007/s10623-012-9763-6

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  • DOI: https://doi.org/10.1007/s10623-012-9763-6

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