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arXiv · 1301.6231

Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes

Alexander Zeh·Antonia Wachter-Zeh·Maximilien Gadouleau·Sergey Bezzateev
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Abstract

Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved. Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them.

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Alexander Zeh, Antonia Wachter-Zeh, Maximilien Gadouleau, Sergey Bezzateev. 2013-01-26. Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes. https://arxiv.org/abs/1301.6231

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