Three-valued Gauss periods, circulant weighing matrices and association schemes
Three-valued Gauss periods, circulant weighing matrices and association schemes
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DOI：
10.1007/s10801-016-0664-z
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发表时间：
2016-01
影响因子：
0.8
通讯作者：
Tao Feng;K. Momihara;Qing Xiang
中科院分区：
文献类型：
--
作者：
Tao Feng;K. Momihara;Qing Xiang
恰好取两个值的高斯周期与二重不可约循环码和强正则凯莱图密切相关。施密特和怀特等人的工作对它们进行了广泛的研究。在本文中，我们考虑高斯周期何时恰好取三个有理值的问题。我们获得了高斯周期恰好取三个有理值的数值必要条件。我们证明，在某些情况下，获得的必要条件也是充分的。我们给出了许多例子，其中高斯周期恰好取三个值。此外，我们讨论了三值高斯周期和组合结构（例如循环权重矩阵和三类关联方案）之间的联系。
Gauss periods taking exactly two values are closely related to two-weight irreducible cyclic codes and strongly regular Cayley graphs. They have been extensively studied in the work of Schmidt and White and others. In this paper, we consider the question of when Gauss periods take exactly three rational values. We obtain numerical necessary conditions for Gauss periods to take exactly three rational values. We show that in certain cases, the necessary conditions obtained are also sufficient. We give numerous examples where the Gauss periods take exactly three values. Furthermore, we discuss connections between three-valued Gauss periods and combinatorial structures such as circulant weighing matrices and three-class association schemes.