Some notes on d-form functions with difference-balanced property

Abstract

The relation between a cyclic relative difference set and a cyclic difference set is considered. Both the sets are with Singer parameters and can be constructed from a difference-balanced d-form function. Although neither of the inversions of Klapper A.′s and No J. S.′s main theorems is true, we prove that a difference-balanced d-form function can be obtained by the cyclic relative difference set and the cyclic difference set introduced by these two main theorems respectively. © Springer-Verlag Berlin Heidelberg 2007.