On the efficiency of shortened cyclic single-burst-correcting codes
IEEE Transactions on Information Theory
| Hi-index | 754.90 |
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 $1leq kleq n$ 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.