Note: Difference set constructions of DRADs and association schemes

  • Authors:

  • James A. Davis;John Polhill

  • Affiliations:

  • Department of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173, United States;Department of Mathematics, Computer Science, and Statistics, Bloomsburg University, Bloomsburg, PA 17815, United States

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

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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 Z"2"^"r^2 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.