Year: 2022
Author: Yue Zhou
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 123–135
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0049
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 123–135
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Partial difference set strongly regular graph finite field