MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS

Abstract

In this paper we introduce a level weight enumerator for linear binary codes whose index set is a forest. This weight enumerator gives most of the weight enumerators as a special case by specializing its variables. We prove a MacWilliams identity for this weight enumerator over this special family of posets which also generalizes the previous results in literature. Further, both the code and its dual are considered over this family of posets using the definition of this weight enumerator which was not possible before. We conclude by an illustrative example and some remarks.