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

Authors:
Wei-Hung Liu;Yu Qing Chen;K. J. Horadam
Affiliations:
School of Mathematical and Geospatial Sciences, RMIT-City Campus, Melbourne, VIC, Australia;Department of Mathematics and Statistics, Wright State University, Dayton, OH;School of Mathematical and Geospatial Sciences, RMIT-City Campus, Melbourne, VIC, Australia
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

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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 Z/4Z is constructed. The methods we use are character theory of abelian groups and Galois rings over Z/4Z.