Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums

Details Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums

2012-02-28

arxiv.org/abs/1202.6414v1

Mathematics

Combinatorics

19 pages

Scientific paper

In this paper, we give constructions of strongly regular Cayley graphs and skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and our results generalize ten of the eleven sporadic examples of cyclotomic strongly regular graphs given by Schmidt and White [24] and several of subfield examples into infinite families. These infinite families of strongly regular graphs have new parameters. The main tools that we employed are relative Gauss sums instead of explicit evaluations of Gauss sums.

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