Relative difference sets fixed by inversion (ii)—character theoretical approach

Abstract

In this paper, we continue our investigation of relative difference sets fixed by inversion. We exclusively focus our attention on abelian groups. New necessary conditions are obtained and a new family of such relative difference sets with forbidden subgroup $\mathbb{Z}/4\mathbb{Z}$ is constructed. The methods we use are character theory of abelian groups and Galois rings over $\mathbb{Z}/4\mathbb{Z}$.