An alternative construction of the Hermitian unital 2‐(28, 4, 1) design

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-09-26 DOI:10.1002/jcd.21861

Koichi Inoue

引用次数: 0

Abstract

In this paper, we give an alternative construction of the Hermitian unital 2‐(28, 4, 1) design in such a way that it is constructed on the isotropic vectors in a unitary geometry of dimension 3 over the field F 4 ${{\mathbb{F}}}_{4}$ . As a corollary, we can construct a unique 3‐(10, 4, 1) design (namely, the Witt system W 10 ${{\boldsymbol{W}}}_{{\bf{10}}}$ ).

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厄米单位2‐(28,4,1)设计的另一种结构

在本文中，我们给出了厄密单位2‐(28,4,1)设计的另一种构造，这种构造是在域f4 ${{\mathbb{F}}}_{4}$上的3维酉几何中的各向同性向量上构造的。作为推论，我们可以构造一个唯一的3‐(10,4,1)设计(即Witt系统W 10 ${{\boldsymbol{W}}}_{{\bf{10}}}$)。

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

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.