On Quasi-Hermitian Varieties in Even Characteristic and Related Orthogonal Arrays

IF 0.5 4区 数学 Q3 MATHEMATICS
Angela Aguglia, Luca Giuzzi, Alessandro Montinaro, Viola Siconolfi
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引用次数: 0

Abstract

In this article, we study the BM quasi-Hermitian varieties, laying in the three-dimensional Desarguesian projective space of even order. After a brief investigation of their combinatorial properties, we first show that all of these varieties are projectively equivalent, exhibiting a behavior which is strikingly different from what happens in odd characteristic. This completes the classification project started there. Here we prove more; indeed, by using previous results, we explicitly determine the structure of the full collineation group stabilizing these varieties. Finally, as a byproduct of our investigation, we also construct a family of simple orthogonal arrays O ( q 5 , q 4 , q , 2 ) , with entries in F q , where q is an even prime power. Orthogonal arrays (OA's) are principally used to minimize the number of experiments needed to investigate how variables in testing interact with each other.

偶特征正交阵列中的拟厄米变换
在本文中,我们研究了放置在偶数阶三维德格鲁投影空间中的BM类厄密变体。在对它们的组合性质进行了简短的研究之后,我们首先表明,所有这些变体都是射影等效的,表现出一种与奇数特征截然不同的行为。这样就完成了从那里开始的分类项目。这里我们证明了更多;事实上,通过使用先前的结果,我们明确地确定了稳定这些品种的全共直群的结构。最后,作为我们调查的副产品,我们还构造了一个简单正交阵列O (q5)族, q4, q,2),项在fq中,其中q是偶素数幂。正交阵列(OA’s)主要用于减少研究测试变量如何相互作用所需的实验数量。
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来源期刊
CiteScore
1.60
自引率
14.30%
发文量
55
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.
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