特征≠2的有限奇异正交几何中的计数定理和一类PBIB设计

TWO ENUMERATION THEOREMS IN SINGULAR ORTHOGONAL GEOMETRY OVER FINITE FIELD OF Ch.≠2 AND A CLASS OF PBIB DESIGNS

特征≠２的有限奇异正交几何中的计数定理和一类ＰＢＩＢ设计魏鸿增（河北师范学院数学系，石家庄０５００９１）ＴＷＯＥＮＵＭＥＲＡＴＩＯＮＴＨＥＯＲＥＭＳＩＮＳＩＮＧＵＬＡＲＯＲＴＨＯＧＯＮＡＬＧＥＯＭＥＴＲＹＯＶＥＲＦＩＮＩＴＥＦＩＥＬＤＯＦＣｈ．≠２Ａ...

Let Fq be a finite field with q elements, where q is a power of an odd prime. In this paper, the number of subspaces in a transitive set contained in a given subspace of the singular orthogonal geometry over Fq is computed. Then using a class of 1-dimensional isotropic subspaces as elements, some PBIB designs are also constructed.