一类函数及其在构建半对称设计中的应用

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

Designs, Codes and Cryptography Pub Date : 2024-07-20 DOI:10.1007/s10623-024-01455-1

Robert S. Coulter, Bradley Fain

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引用次数: 0

摘要

我们引入了指数为 \(\lambda \)的半平面函数的概念，概括了之前的几个概念。我们展示了如何利用半平面函数来构造由函数决定的入射结构的半对称性设计。然后，我们考虑了有关结构连接性的问题。通过建立有限域上的单项式范例，我们解决了存在性问题，并研究了线性化多项式的组合如何带来更多范例。最后，我们将回到入射结构，并考虑当入射结构使用某一类函数构建时的最大交集。

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A class of functions and their application in constructing semisymmetric designs

We introduce the notion of a semiplanar function of index \(\lambda \), generalising several previous concepts. We show how semiplanar functions can be used to construct semisymmetric designs using an incidence structure determined by the function. Issues regarding the connectivity of the structure are then considered. The question of existence is addressed by establishing monomial examples over finite fields, and we examine how composition with linearized polynomials can lead to further classes of examples. We end by returning to the incidence structure and considering maximal intersection sets when the incidence structure is constructed using a particular class of functions.

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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.