Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes

2012/01/03 by Tao Feng, Feng, Tao, Koji Momihara +3
Computer Science · Engineering · Mathematics · #05B10 #05E30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1201.0701

openalex publication_date 2012/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 in finite fields, and they generalize the constructions given by Feng and Xiang \citeFX111,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.

Citations

• Pseudocyclic and non-amorphic fusion schemes of the cyclotomic association schemes
• Strongly Regular Graphs From Unions of Cyclotomic Classes

Related

• Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums
• Skew Hadamard difference sets from cyclotomic strongly regular graphs
• Strongly Regular Graphs From Unions of Cyclotomic Classes
• Constructions of Strongly Regular Cayley Graphs Using Index Four Gauss Sums
• Constructions of Strongly Regular Cayley Graphs using Even Index Gauss Sums