利用特征为2域上伪辛几何中1维非迷向子空间构作PBIB设计

Using 1-Dimensional Non-Isotropic Subspaces in Pseudo-Symplectic Geometry over Finite Fields of Characteristic 2 to Construct a class of PBIB Designs

<正> 关于结合方案和PBIB设计的定义及所用的有关符号见文献[1].设F_q为特征为2的有限域,q=2~r.熟知F_q上的对称矩阵合同于以下三种形式的矩阵(见[1]p.24).

Let Fq be a finite field of characteristic 2. Taking K = (oI(v)i(v)o) + (0111),we define a group C and a relative geometry by K. In this paper, we take the set of all 1-dimensional non-isotropic subspaces over Fq as the set of treatments to construct an association scheme and PBIB designs with three associative classes. The parameters concerning the designs are also computed.