Signed difference sets

被引：1

作者：

Gordon, Daniel M. ^{[1
]}

机构：

[1] IDA Ctr Commun Res, 4320 Westerra Court, San Diego, CA 92121 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 05期

关键词：

Difference sets; Circulant weighing matrices; Two-level autocorrelation;

D O I：

10.1007/s10623-022-01171-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A (v, k, lambda) difference set in a group G is a subset {d(1), d(2), . . . , dk} of G such that D = Sigma d(i) in the group ring Z[G] satisfies DD-1 = n + lambda G where n= k - lambda. If D = Sigma s(i)d(i), where the s(i) is an element of{+/- 1}, satisfies the same equation, we will call it a signed difference set. This generalizes both difference sets (all s(i) = 1) and circulant weighing matrices (G cyclic and lambda = 0). We will show that there are other cases of interest, and give some results on their existence.

引用

页码：2107 / 2115

页数：9

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