Two-dimensional array codes correcting rectangular burst errors

Two-dimensional array codes correcting rectangular burst errors are considered. We give a construction and examples of linear two-dimensional array codes correcting rectangular burst errors of size b ₁ × b ₂ with minimum redundancy r = 2b ₁ b ₂. We present constructions of cyclic two-dimensional array codes correcting phased and arbitrary rectangular burst errors; their encoding and decoding algorithms are also given. A class of cyclic two-dimensional array codes correcting rectangular burst errors with asymptotically minimal redundancy is described. We construct a class of linear two-dimensional array codes correcting cyclic rectangular b ₁ × b ₂ burst errors with asymptotic excess redundancy $\tilde r_C (b_1 ,b_2 ) = 2b_1 b_2 - 3$ .