Two-dimensional cyclic codes over a finite chain ring

Abstract In this paper, we have determined the generators and rank of a 2D cyclic code of length mn over a finite chain ring ℛ with residue field 𝔽 q , where m is arbitrary and q ≡ 1( mod n ). Further, we have obtained a necessary and sufficient condition for a 2D cyclic code over a finite chain ring ℛ to be MHDR. Some examples of 2D cyclic codes have been constructed and ranks of these 2D cyclic codes have been calculated by us. We have also given a few examples of 2D cyclic codes over some finite chain rings, which are MHDR.