Macwilliams identities of the linear codes over Z₄[u,v]/⟨u²,v²,uv,vu⟩

Abstract

In this paper, complete weight enumerators, the symmetrized weight enumerators and the Lee weight enumerators for the linear codes over the ring S = Z₄ +uZ₄ +vZ₄, where u² = v² = uv = vu = 0 are defined. The MacWilliams identity denotes an identity between a linear code and its dual code on their weight distribution. We classify elements of S into seven classes and study MacWilliams identities of linear codes over S. Finally, we calculate the Lee weights of Gray images of the elements and give an example.