Paley type partial difference sets in abelian groups
Document Type
Article
Publication Date
11-16-2019
Department
Department of Mathematical Sciences
Abstract
Partial difference sets with parameters (π£,π,π,π)=(π£,(π£β1)/2,(π£β5)/4,(π£β1)/4) are called Paley type partial difference sets. In this note, we prove that if there exists a Paley type partial difference set in an abelian group of order v, where v is not a prime power, then π£=π4 or 9π4 , π>1 an odd integer. In 2010, Polhill constructed Paley type partial difference sets in abelian groups with those orders. Thus, combining with the constructions of Polhill and the classical Paley construction using nonzero squares of a finite field, we completely answer the following question: βFor which odd positive integers π£>1 , can we find a Paley type partial difference set in an abelian group of order π£ ?β
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Wang, Z.
(2019).
Paley type partial difference sets in abelian groups.
Journal of Combinatorial Designs,
28(2), 149-152.
http://doi.org/10.1002/jcd.21691
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1525