Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance
Abstract
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time probabilistic burst error decoding procedure based on the third bound is outlined. Index Terms Bound on the minimum distance, burst error, efficient decoding, folded code, repeated-root cyclic code, repeated-root cyclic product code
Cite
@article{arxiv.1506.02820,
title = {Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance},
author = {Alexander Zeh and Markus Ulmschneider},
journal= {arXiv preprint arXiv:1506.02820},
year = {2015}
}