Abstract For codes over Z m , pomset metric is a generalization to poset metric, in some sense. We define pomset weight enumerator of a code C and establish MacWilliams type identities for linear codes with respect to certain pomsets. The identities for a particular type of linear codes (those that can be described as direct sum of linear codes) are established by considering direct and ordinal sum of pomsets on them. By induction, this result is extended for more than two pomsets. Moreover, MacWilliams type identities for any linear code with chain pomset is derived which paved a way to arrive at those identities for direct sum of codes with disjoint union of chains.

中文翻译：

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某些 pomsets 上线性代码的 MacWilliams 类型标识：pomsets 的链、直接和序数总和

Abstract 对于 Z m 上的代码，从某种意义上说，pomset 度量是对poset 度量的推广。我们定义代码 C 的 pomset 权重枚举器，并针对某些 pomset 建立线性代码的 MacWilliams 类型标识。特定类型的线性码（可以描述为线性码的直接和）的身份是通过考虑它们上的直接和序数和来建立的。通过归纳，这个结果被扩展到两个以上的 pomsets。此外，推导出具有链 pomset 的任何线性代码的 MacWilliams 类型身份，这为获得具有不相交链并集的代码的直接和的那些身份铺平了道路。