Classification of Poset-Block Spaces Admitting MacWilliams-Type Identity
In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical, and at any level of the poset, all the blocks have the same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the weight enumerators of a code and its dual.
macwilliams-type identity macwilliams identity poset-block codes weight distribution