“…In the case of poset metrics, to attain such a relation one needs to consider the dual poset: given a poset P = ([n], P ), the dual poset is the poset P = ([n], P ) defined by the opposite relations, i.e., given i, j ∈ [n], then For poset metrics, the MacWilliams Identity was first investigated in [19]. In [4] it was proved that the hierarchical posets are the only posets admitting a MacWilliams' identity, furthermore, explicit formulae for those identities was obtained.…”