MACWILLIAMS IDENTITIES OF THE LINEAR CODES OVER Z4[u,v] ⟨u2,v2,uv,vu⟩

MACWILLIAMS IDENTITIES OF THE LINEAR CODES OVER Z4[u,v] ⟨u2,v2,uv,vu⟩

B. Çalışkan

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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.

Keywords

Gray map, linear codes, MacWilliams identities, weight enumerators.