利用交错矩阵和Hermite矩阵构作BIB设计

Applications of Alternating Matrices and Hermitian Matrices to the Construction of BIB Designs

本文给出了有限域上交错矩阵与Hermite 矩阵的一些计数结果,然后利用V_n(F_q)中的一类子空间作元素,F_q 上交错矩阵或Hermite 矩阵的等同类作区组构作BIB 设计,并计算了它们的参数.

In this paper,enumeration results of alternating matrices and Her-mitian matrices over finite fields are obtained.With a certain class of subspacesof V_n(F_q)as elements,and the equivalent classes of nonsingular alternating matricesor Hermitian matrices over F_q as blocks,a series of BIB designs are constructedand their parameters are calculated.