Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-01-07 , DOI: 10.1016/j.disc.2019.111782
Gnana Sudha Irrinki; Selvaraj R.S.

For codes over ${\mathbb{Z}}_{m}$, pomset metric is a generalization to poset metric, in some sense. We define pomset weight enumerator of a code $\mathcal{C}$ 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.

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