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 $b_1\times b_2$ with minimum redundancy $r=2b_1b_2$. 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 $b_1\times b_2$ burst errors with asymptotic excess redundancy $\tilde r_C(b_1,b_2)=2b_1b_2-3$.