MDS and I-Perfect Codes in Pomset block Metric
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In this paper, we establish the Singleton bound for pomset block codes ((Pm,π)-codes) of length N over the ring ℤ_m. We give a necessary condition for a code to be MDS in the pomset (block) metric and prove that every MDS (Pm,π)-code is an MDS (P,π)-code. Then we proceed on to find I-perfect and r-perfect codes. Further, given an ideal with partial and full counts, we look into how MDS and I-perfect codes relate to one another. For chain pomset, we obtain the duality theorem for pomset block codes of length N over ℤ_m; and, the weight distribution of MDS pomset block codes is then determined.
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