Constructing linked systems of relative difference sets via Schur rings

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-16 DOI:10.1007/s10623-024-01406-w

Mikhail Muzychuk, Grigory Ryabov

引用次数: 0

Abstract

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 \(p^2\). All constructions of new RDSs and their linked systems make usage of cyclotomic Schur rings.

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通过舒尔环构建相对差集的关联系统

本文研究相对差集（RDS）及其关联系统。研究表明，一个封闭的 RDS 链接系统总是被一个群分级。基于这一结果，我们还定义了共享相同分级群的 RDS 链接系统的乘积。此外，我们还推广了 RDS 链接系统的戴维斯-波尔希尔-史密斯构造。最后，我们在有限域上的海森堡群中构造了新的 RDS 关联系统，并在指数为 \(p^2\) 的外特殊 p 群中构造了 RDS 族。所有新 RDS 及其链接系统的构建都使用了环舒尔环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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