Amorphic association schemes with negative Latin square-type graphs

Authors:
James A. Davis;Qing Xiang
Affiliations:
Department of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173, USA;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
Finite Fields and Their Applications
Year:
2006

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Abstract

Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square-type graphs and whose underlying set is a nonelementary abelian 2-group. We give a simple proof of a result of Hamilton that generalizes Brouwer's result. We use multiple distinct quadratic forms to construct amorphic association schemes with a large number of classes.