Classification of poset-block spaces admitting MacWilliams-type identity
arXiv:1202.6409 · doi:10.1109/TIT.2012.2210192
Abstract
In this work 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 explicit the relation between the weight enumerators of a code and its dual.
8 pages, 1 figure. Submitted to IEEE Transactions on Information Theory