Constructions of Strongly Regular Cayley Graphs and Skew Hadamard   Difference Sets from Cyclotomic Classes
  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. 
Tao Feng, Koji Momihara, Qing Xiang
math.CO