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On the Nonexistence of Partial Difference Sets by Projections to Finite Fields

On the Nonexistence of Partial Difference Sets by Projections to Finite Fields

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.

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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

Author Details

Yue Zhou