@Article{CMR-38-2,
author = {Zhou, Yue},
title = {On the Nonexistence of Partial Difference Sets by Projections to Finite Fields},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {38},
number = {2},
pages = {123--135},
abstract = {<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>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2020-0049},
url = {https://global-sci.com/article/81480/on-the-nonexistence-of-partial-difference-sets-by-projections-to-finite-fields}
}