摘要
取F_q上n维向量空间中m维子空间的集合,1≤m<n,并进行集合处理,Bancheng这样定义了几个结合类的结合方案,计算了它的参数。本文在此结合方案的基础上,在F_q上取n×n非奇斜对称集合矩阵作为区组的集合,给出了PBIB设计,并利用代数方法算出了其参数。
Taking the set of m-dimenional subspaces of an n-dimensional vector apace overF_q, wnere 1≤m<n, as the set of treatments, Bancheng defined an association scheme withsevreal associate classes and computed its parameters. In the present paper, based on thisassociation scheme and taking the set n×n nonsingular skew-symmetric matrices over F_qas the set of blocks, a PBIB design is defined and its parameters are computed by alge-braic method.
关键词
向量空间
结合方案
PBIB设计
Finite field
vector space
association scheme
nonsingular skew-symmetric matrix
PBIB design
