Duality in $l_{p\gamma }$-spaces

Abstract

Codes in $l_{p\gamma }$-spaces, introduced by the author in [3], are a natural generalization of one-dimensional codes in $RT$-spaces [6] to block coding and have applications in different areas of combinatorial/discrete mathematics, e.g., in the theory of uniform distribution, experimental designs, cryptography, etc. In this paper, we introduce various types of weight enumerators in $l_{p\gamma }$-codes, viz., exact weight enumerator, complete weight enumerator, block weight enumerator, and $\gamma$-weight enumerator. We obtain the MacWilliams duality relation for the exact and complete weight enumerators of an $l_{p\gamma }$-code.