Achieving the Reiger bound for burst errors using two-dimensional interleaving schemes

The Reiger bound states that the redundancy n-log_qM of any q-ary code, of M codewords of n letters each, that corrects bursts of size up to B is at least 2B (assuming that there are two disjoint bursts of size B that can be corrected by the code (Bossert and Sidorenko, 1996; and Reiger, 1960). In order to achieve the Reiger bound by interleaving single error-correcting codes, these codes should be MDS and the interleaving scheme should use only B of them. Such interleaving is straightforward in one-dimension. Here we consider the two-dimensional version of this problem