TY - JOUR
T1 - On the Nonexistence of Partial Difference Sets by Projections to Finite Fields
AU - Zhou , Yue
JO - Communications in Mathematical Research 
VL - 2
SP - 123
EP - 135
PY - 2022
DA - 2022/02
SN - 38
DO - http://doi.org/10.4208/cmr.2020-0049
UR - https://global-sci.org/intro/article_detail/cmr/20267.html
KW - Partial difference set, strongly regular graph, finite field
AB - <p style="text-align: justify;">In the study of (partial) difference sets and their generalizations in
groups $G$, the most widely used method is to translate their definition into an
equation over group ring $\mathbb{Z}[G]$ and to investigate this equation by applying
complex representations of $G.$ In this paper, we investigate the existence of
(partial) difference sets in a different way. We project the group ring equations
in $\mathbb{Z}[G]$ to $\mathbb{Z}[N]$ where $N$ is a quotient group of $G$ isomorphic to the additive
group of a finite field, and then use polynomials over this finite field to derive
some existence conditions.</p>