Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes (1201.0701v1)

Published 3 Jan 2012 in math.CO

Abstract: In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions given by Feng and Xiang \cite{FX111,FX113}. Three infinite families of strongly regular graphs with new parameters are obtained. The main tools that we employed are index 2 Gauss sums, instead of cyclotomic numbers.

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