Constructing linked systems of relative difference sets via Schur rings

被引：0

作者：

Muzychuk, Mikhail ^{[1
]}

Ryabov, Grigory ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Beer Sheva, Israel

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2024年 / 92卷 / 09期

基金：

以色列科学基金会;

关键词：

Relative difference sets; Linked systems; Schur rings; ASSOCIATION SCHEMES; LINKING SYSTEMS; (P(A); P(B); P(A);

D O I：

10.1007/s10623-024-01406-w

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems sharing the same grading group. Further, we generalize the Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we construct new linked system of RDSs in a Heisenberg group over a finite field and family of RDSs in an extraspecial p-group of exponent p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p<^>2$$\end{document}. All constructions of new RDSs and their linked systems make usage of cyclotomic Schur rings.

引用

页码：2615 / 2637

页数：23

共 37 条

[1]

[Anonymous], 2003, St. Petersburg Math. J., V14, P189

[2] DIVISIBLE DIFFERENCE SETS WITH MULTIPLIER -1 [J].