Two-dimensional burst-correcting codes

We consider two-dimensional error-correcting codes capable of correcting unrestricted bursts of size b. We construct optimal 2-burst-correcting codes in three connectivity models: the rectangular grid with 4 or 8 neighbors, and the hexagonal graph. We also give optimal, or nearly optimal. 2-burst-correcting codes in all dimensions. We then construct 3-burst-correcting codes with 3 redundancy bits above the sphere-packing bound, followed by b-straight-burst-correcting codes with b - 2 redundancy bits above the sphere-packing bound. We conclude by improving the Reiger bound for two-dimensional unrestricted-burst-correcting codes.