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

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• 作者：Tao Feng ; Koji Momihara ; Qing Xiang
• 关键词：05B10 ; 05E30
• 刊名：Combinatorica
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：35
• 期：4
• 页码：413-434
• 全文大小：533 KB
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• 作者单位：Tao Feng (1)
  Koji Momihara (2)
  Qing Xiang (3)
  
  1. Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, China
  2. Faculty of Education, Kumamoto University, 2-40-1 Kurokami, Kumamoto, 860-8555, Japan
  3. Department of Mathematical Science, University of Delaware, Newark, DE, 19716, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1439-6912

文摘

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. Mathematics Subject Classification (2000) 05B10 05E30