A common generalization of hypercube partitions and ovoids in polar spaces

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

Designs, Codes and Cryptography Pub Date : 2024-09-17 DOI:10.1007/s10623-024-01489-5

Jozefien D’haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt

引用次数: 0

Abstract

We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a generalization of ovoids in polar spaces as well as the natural q-analog of a subcube partition of the hypercube (which can be seen as a polar space with \(q=1\)). Our main result proves that a generalized ovoid of k-spaces in polar spaces of large rank does not exist.

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极地空间中的超立方体分区和卵形体的通用概括

我们研究所谓的广义敖包，即有限经典极性空间的完全各向同性子空间族，使得每个最大完全各向同性子空间恰好包含该族的一个成员。这是极性空间中的敖包的广义化，也是超立方体的子立方体分区的自然 q-analog （可以看作是具有（q=1\）的极性空间）。我们的主要结果证明了在大秩的极空间中不存在k空间的广义卵形。

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

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.