{"title":"有限域上投影的偏差分集的不存在性","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":"{\"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}","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}
On the Nonexistence of Partial Difference Sets by Projections to Finite Fields
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