{"title":"On the Nonexistence of Partial Difference Sets by Projections to Finite Fields","authors":"Yue Zhou","doi":"10.4208/cmr.2020-0049","DOIUrl":null,"url":null,"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 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. AMS subject classifications: 05B10, 05E30, 11T06","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2020-0049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 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. AMS subject classifications: 05B10, 05E30, 11T06