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.