Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes
Information Theory
2013-06-28 v2 math.IT
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.
Cite
@article{arxiv.1301.6231,
title = {Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes},
author = {Alexander Zeh and Antonia Wachter-Zeh and Maximilien Gadouleau and Sergey Bezzateev},
journal= {arXiv preprint arXiv:1301.6231},
year = {2013}
}
Comments
5 pages, no figure, accepted for ISIT2013