Article ID Journal Published Year Pages File Type
4648499 Discrete Mathematics 2012 14 Pages PDF
Abstract

The MacWilliams identity for the complete m-spotty weight enumerators of byte-organized binary codes is a generalization of that for the Hamming weight enumerators of binary codes. In this paper, Jacobi forms are obtained by substituting theta series into the complete m-spotty weight enumerators of binary Type II codes. The Mellin transforms of those theta series provide functional equations for partial Epstein zeta functions which are summands of classical Epstein zeta functions associated with quadratic forms. Then, it is observed that the coefficient matrices appearing in those functional equations are exactly the same as the transformation matrices in the MacWilliams identity for the complete m-spotty weight enumerators of binary self-dual codes.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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