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

作　　者：Yue Zhou 

机构地区：[1]Department of Mathematics,National University of Defense Technology,Changsha 410073,China

出　　处：《Communications in Mathematical Research》2022年第2期123-135,共13页数学研究通讯（英文版）

基　　金：This work is partially supported by Natural Science Foundation of Hunan Province(No.2019JJ30030);Training Program for Excellent Young Innovators of Changsha(No.kql905052).

摘　　要：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 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 Z[G]to 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.

关 键 词：Partial difference set strongly regular graph finite field 

分 类 号：O17[理学—数学]