A survey of partial difference sets
Designs, Codes and Cryptography
Some New Cyclotomic Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
Finite fields
Cyclotomy and Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
Pseudocyclic association schemes and strongly regular graphs
European Journal of Combinatorics
Cyclotomic constructions of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Strongly regular graphs from unions of cyclotomic classes
Journal of Combinatorial Theory Series B
Finite Fields and Their Applications
All Two-Weight Irreducible Cyclic Codes?
Finite Fields and Their Applications
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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. Our results generalize ten of the eleven sporadic examples of cyclotomic strongly regular graphs given by Schmidt and White (2002) [23] and several 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.