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arXiv · 0712.2182

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

Henk D. L. Hollmann·Ludo M. G. M. Tolhuizen
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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.

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Henk D. L. Hollmann, Ludo M. G. M. Tolhuizen. 2007-12-13. Optimal codes for correcting a single (wrap-around) burst of errors. https://arxiv.org/abs/0712.2182

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