New necessary conditions on Paley‐type partial difference sets in abelian groups
Let be an abelian group of order , where are distinct odd prime numbers. In this paper, we prove that if contains a regular Paley‐type partial difference set (PDS), then for any is congruent to 3 modulo 4 whenever is odd. These new necessary conditions further limit the specific order of an abelian group in which there can exist a Paley‐type PDS. Our result is similar to a result on abelian Hadamard (Menon) difference sets proved by Ray‐Chaudhuri and Xiang in 1997.
Journal of Combinatorial Designs
New necessary conditions on Paley‐type partial difference sets in abelian groups.
Journal of Combinatorial Designs.
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© 2019 Wiley Periodicals, Inc. Publisher's version of record: https://doi.org/10.1002/jcd.21655