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Pomset block metric is a generalization of pomset metric. In this paper, wedefine weight enumerator of linear block codes in pomset metric over$\mathbb{Z}_m$ and establish MacWilliams type identities for linear block codeswith respect to certain pomsets. The relation between weight enumerators of twolinear pomset block codes and their direct sum is also investigated.

MacWilliams Type Identities for Linear Block Codes on Certain Pomsets