Difference set constructions of DRADs and association schemes |
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Authors: | James A Davis |
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Institution: | a Department of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173, United States b Department of Mathematics, Computer Science, and Statistics, Bloomsburg University, Bloomsburg, PA 17815, United States |
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Abstract: | Doubly Regular Asymmetric Digraphs (DRAD) with rank 4 automorphism groups were previously thought to be rare. We exhibit difference sets in Galois Rings that can be used to construct an infinite family of DRADs with rank 4 automorphism groups. In addition, we construct difference sets in groups for all r?2 that can be used to construct DRADs and nonsymmetric 3-class imprimitive association schemes. Finally, we prove a new product construction for difference sets so that the resulting difference sets can be used to build nonsymmetric 3-class imprimitive association schemes. |
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Keywords: | Regular asymmetric digraph Nonsymmetric imprimitive association schemes Galois Rings Hadamard difference sets |
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