利用伪辛空间中的迷向点集构作结合方案(英文)  

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM THE SET OF ISOTROPIC POINTS IN PSEUDO SYMPLECTIC SPACES

作　　者：王恺顺[1] 魏鸿增[1] 

机构地区：[1]河北师范大学

出　　处：《数学杂志》1998年第2期225-228,共4页Journal of Mathematics

摘　　要：令Ｆｑ是ｑ个元的有限域，其中ｑ是一个２的方幂。在本文我们假设δ＝１或２。一个２υ＋δ维的射影空间ＰＧ（２υ＋δ，Ｆｑ）可以划分为一个２υ＋δ维仿射空间和一个无穷远超平面Ｈ的并。Ｈ中的点分为两部分：２υ＋δ维伪辛空间迷向点集Ｍ２υ＋δ－２和非迷向点集Ｍ′２υ＋δ－２。定义仿射空间中点ａ和ｂ具有第ｉ种结合关系，如果线ａｂ交Ｈ于第ｉ个子集。我们证明了上述构作为一个两个类的结合方案。最后，利用一般的代数方法也构作出３个类的结合方案。Let F q be a finite field with q elements, where q is a power of 2. In this paper, we assume that δ=1 or 2, and consider a projective space PG(2υ+δ,F q), partitioned into an affine space of dimension 2υ+δ and a hyperplane H of dimension 2υ+δ-1 at infinity. The points of the hyperplane H are next partitioned into 2 subsets—the set M 2υ+δ-2  of isotropic points and the set M′ 2υ+δ-2  of non isotropic points of a (2υ+δ) dimensional Pseudo Symplectic space. A pair of points a and b of the affine space is defined to belong to class i if the line  ab  meets the subset i of H. In this case, we show that the classification of pairs of affine points defines a two class association scheme. Finally, using a general algebraic method, we have also derived a three class association scheme.

关 键 词：结合方案 伪辛空间 伪辛几何 迷向点集 

分 类 号：O157.3[理学—数学]