MacWilliams Type Identities for Linear Block Codes on Certain Pomsets

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