Optimal codes for correcting a single (wrap-around) burst of errors

Details Optimal codes for correcting a single (wrap-around) burst of errors Optimal codes for correcting a single (wrap-around) burst of errors

2007-12-13

arxiv.org/abs/0712.2182v1

Computer Science

Information Theory

10 pages; submitted to IEEE Transactions on Information Theory

Scientific paper

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.

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