利用仿射辛几何构作结合方案与PBIB设计

Construction of association schemes and PBIB designs by affine Symplectic geometry

把有限域上的辛群的研究推广到仿射辛群并对仿射辛群的可迁性进行了研究 .利用矩阵的技巧和方法 ,证明了仿射辛群双可迁地作用在仿射辛几何中的仿射极大全迷向子空间上 ,并且给出了轨道的明确表示 .作为该理论的一个应用 ,利用仿射辛几何中的极大全迷向子空间的全体作为处理集构作了一个多个结合类的结合方案和PBIB设计 ,并计算了所有的参数 .

Classical group is the main part of group theory research. Symplectic group research is enlarged in the finite field to the affine Symplectic group by studying the transition of affine Symplectic group. It is proved by matrix technique and ways that affine Symplectic groups have double transition on the affine maximal and total isotropic subspaces over affine Symplectic geometry and their orbits are described. As an application affine maximal and total isotropic subspaces are used to construct several classes of association schemes and PBIB designs, and calculate all the parameters.