有限域上投影的偏差分集的不存在性

数学研究通讯 Pub Date : 2022-01-01 DOI:10.4208/cmr.2020-0049

Yue Zhou

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引用次数: 0

摘要

在群G中的(偏)差分集及其推广的研究中，最常用的方法是将其定义转化为群环Z上的方程[G]，并利用G的复表示来研究这个方程。本文用另一种方法研究了(偏)差分集的存在性。我们将Z[G]中的群环方程投影到Z[N]上，其中N是G同构于有限域的加性群的商群，然后利用有限域上的多项式推导出存在条件。AMS学科分类:05B10, 05E30, 11T06

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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

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数学研究通讯

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1035