In this paper all poset structures are classi£ed which admit the MacWilliams identity, and the MacWilliams identities for poset weight enumerators corresponding to such posets are derived. We prove that being a hierarchical poset is a necessary and suf£cient condition for a poset to admit MacWilliams identity. An explicit relation is also derived between P-weight distribution of a hierarchical poset code and P-weight distribution of the dual code.

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