Optimal codes for correcting a single (wrap-around) burst of errors
Information Theory
2007-12-14 v1 math.IT
Abstract
In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n,k] codes that can correct any burst of erasures (including wrap-around bursts) of length n-k. The raised the question if such [n,k] codes exist for all integers k and n with 1<= k <= n and all fields (in particular, for the binary field). In this note, we answer this question affirmatively by giving two recursive constructions and a direct one.
Cite
@article{arxiv.0712.2182,
title = {Optimal codes for correcting a single (wrap-around) burst of errors},
author = {Henk D. L. Hollmann and Ludo M. G. M. Tolhuizen},
journal= {arXiv preprint arXiv:0712.2182},
year = {2007}
}
Comments
10 pages; submitted to IEEE Transactions on Information Theory