Pseudocyclic and non-amorphic fusion schemes of the cyclotomic association schemes

Authors:
Tao Feng;Fan Wu;Qing Xiang
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, USA 19716 and Department of Mathematics, Zhejiang University, Hangzhou, China 310027;Department of Mathematical Sciences, University of Delaware, Newark, USA 19716;Department of Mathematical Sciences, University of Delaware, Newark, USA 19716
Venue:
Designs, Codes and Cryptography
Year:
2012

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Cyclotomy, gauss sums, difference sets and strongly regular cayley graphs

SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications

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Abstract

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov's conjecture by Ikuta and Munemasa (Eur J Combin 31:1513---1519, 2010).