English

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

R2 v1 2026-06-21T09:53:46.534Z