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 = P L `=1 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 general Reed-Solomon codes having the same parameters.