CYCLOTOMIC DIFFERENCE SETS IN FINITE FIELDS

被引：3

作者：

Xia, Binzhou ^{[1
,2
]}

机构：

[1] Univ Western Australia, Sch Math & Stat, Crawley, WA 6009, Australia

[2] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

来源：

MATHEMATICS OF COMPUTATION | 2018年 / 87卷 / 313期

关键词：

PROJECTIVE-PLANES;

D O I：

10.1090/mcom/3311

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classical problem of whether mth-powers with or without zero in a finite field F-q form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient conditions are established including those via a system of polynomial equations on Gauss sums. The author thereby solves the problem for even q which is neglected in the literature, and extends the nonexistence list for even m up to 22. Moreover, conjectures toward the complete classification are posed.

引用

页码：2461 / 2482

页数：22

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