论文标题
纯高斯总和和偏斜哈哈德差异集
Pure Gauss sums and skew Hadamard difference sets
论文作者
论文摘要
Chowla〜（1962），McEliece〜（1974），Evans〜（1977，1981）和Aoki〜（1997，2004，2012）研究了高斯总和，其中一些整体功能在理性数字领域。这样的高斯总和称为{\ it pure}。特别是，Aoki（2004）给出了一个必要且充分的条件，使高斯总和在dirichlet字符方面纯化了所涉及的乘法字符的顺序。在本文中，我们研究纯高斯的质量扩展学位$ f $，并根据Aoki定理以$ f = 5,7,9,11,13,17,19,23 $进行分类。此外，鉴于偏斜的hadamard差异集的应用，我们表征了纯高斯总和的特殊子类。根据表征，我们从有限场的循环类别类别提供了偏斜的Hadamard差异集的新结构。
Chowla~(1962), McEliece~(1974), Evans~(1977, 1981) and Aoki~(1997, 2004, 2012) studied Gauss sums, some integral powers of which are in the field of rational numbers. Such Gauss sums are called {\it pure}. In particular, Aoki (2004) gave a necessary and sufficient condition for a Gauss sum to be pure in terms of Dirichlet characters modulo the order of the multiplicative character involved. In this paper, we study pure Gauss sums with odd extension degree $f$ and classify them for $f=5,7,9,11,13,17,19,23$ based on Aoki's theorem. Furthermore, we characterize a special subclass of pure Gauss sums in view of an application for skew Hadamard difference sets. Based on the characterization, we give a new construction of skew Hadamard difference sets from cyclotomic classes of finite fields.
