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：Pomset 区块指标是孔塞特量度的概括。 在本文中,我们定义了以$\mathbb<unk> m$ 以上的孔塞度量表示的线性区块代码的重量数字,并为某些孔塞的线性区块代码确定了MacWilliams类型身份。 也调查了两个线性孔塞区块码的重量计算器与其直接总和之间的关系。</s>