Optimal Codes for Correcting a Single (Wrap-Around) Burst of Erasures
Henk D. L. Hollmann, Ludo Tolhuizen · IEEE Transactions on Information Theory · 2008
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$n-k$. They raised the question if such$[n,k]$codes exist for all integers$k$and$n$with$1\leq k\leq n$and all fields (in particular, for the binary field). In this correspondence, we answer this question affirmatively by giving two recursive constructions and a direct one.