Decoding Cyclic Codes up to a New Bound on the Minimum Distance
Information Theory
2012-03-13 v2 math.IT
Abstract
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special cases of our bound. For some classes of codes the bound on the minimum distance is refined. Furthermore, a quadratic-time decoding algorithm up to this new bound is developed. The determination of the error locations is based on the Euclidean Algorithm and a modified Chien search. The error evaluation is done by solving a generalization of Forney's formula.
Cite
@article{arxiv.1105.1894,
title = {Decoding Cyclic Codes up to a New Bound on the Minimum Distance},
author = {Alexander Zeh and Antonia Wachter and Sergey Bezzateev},
journal= {arXiv preprint arXiv:1105.1894},
year = {2012}
}