通过舒尔环构建相对差集的关联系统

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-04-16 DOI:10.1007/s10623-024-01406-w

Mikhail Muzychuk, Grigory Ryabov

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引用次数: 0

摘要

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。

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Constructing linked systems of relative difference sets via Schur rings

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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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.