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In this paper, we establish the Singleton bound for pomset block codes (Formula: see text-codes) of length Formula: see text over the ring Formula: see text. An upper and a lower bound on the minimum distance of Formula: see text-Maximum distance separable (MDS) codes are derived. Moreover, we prove that an MDS Formula: see text-code is necessarily an MDS Formula: see text-code. We also investigate the relationship between the Formula: see text-perfect codes and Formula: see text-perfect codes. Given an ideal with partial count and full count, we investigate how MDS and Formula: see text-perfect codes relate to one another. Duality theorem is derived for an MDS Formula: see text-code when all the blocks are of same length, and the distribution of codewords among Formula: see text-balls is analyzed as well. Finally, for a chain pomset, we study the maximum distance separability, packing radius and minimum distance of pomset block codes.
Shriwastva et al. (Fri,) studied this question.
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