Codes correcting phased burst erasures

We introduce a family of binary array codes of size t×n, correcting multiple phased burst erasures of size t. The codes achieve maximal correcting capability, i.e., being considered as codes over GF(2 ^t) they are MDS. The length of the codes is n=Σ_l=1 ^L(_l^t) where L is a constant or is slowly growing in t. The complexity of encoding and decoding is proportional to rnmL where r is the number of correctable erasures, and m is the smallest number such that 2^t=1 modulo m. This compares favorably with the complexity of decoding codes obtained from the shortened Reed-Solomon codes having the same parameters