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

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.

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Correspondence to Qing Xiang.

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Feng, T., Momihara, K. & Xiang, Q. Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes. Combinatorica 35, 413–434 (2015). https://doi.org/10.1007/s00493-014-2895-8

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Mathematics Subject Classification (2000)

  • 05B10
  • 05E30