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Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes

Research paper by Tao Feng, Koji Momihara, Qing Xiang

Indexed on: 10 Sep '14Published on: 10 Sep '14Published in: Combinatorica



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 of finite fields, and they generalize the constructions given by Feng and Xiang [10,12]. 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.