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.

翻译：偏序集分组度量是偏序集度量的推广。本文定义$\mathbb{Z}_m$上线性分组码在偏序集度量下的重量枚举函数，并建立关于特定偏序集的线性分组码的MacWilliams型恒等式。此外，还研究了两个线性偏序集分组码及其直和之间的重量枚举函数关系。