酉空间中一类子空间的排列问题与具有纠错能力的d^z-析取矩阵

Arrangement Problem on the Subspace of the Unitary Space and d^z -Disjunct Matrix with Correction Capability

Pooling设计在实践中有着广泛的应用,它的数学模型是d^z-析取矩阵.本文利用酉空间的一类子空间构做了一类新的d^z-析取矩阵.为了讨论此设计的纠错能力,重点研究了酉空间中的一类子空间的排列问题,即对于酉空间F_q^2^((n))上的一个给定的(m,s)型子空间C和一个整数d,找到C的d个(m-1,s-1)型子空间H_1,H_2,…,H_d,使得包含在H_1∪H_2∪…∪H_d中的(r,s-4)型子空间的个数最多,并确定这个数的上界.然后应用此结果,给出了d^z-析取矩阵中反映纠错能力的z值的紧界.

The pooling design has many application in practice.A mathematical model of pooling design is a d^z-disjunct matrix.In this paper,we construct a kind of new d^z-disjunct matrices with the subspaces of the unitary space.In order to discuss the correction capability of the design,we study the following arrangement problem on the subspace of the unitary space.For a given subspace C of type（m,s） in unitary space F_q^2^（（n）） and an integer d,we find d subspaces of type（m-1,s-1）,H_1,H_2,...,H_d of C that maximize the number of the subspaces of type（r,s - 4） contained in H-1 U H_2 U…U H_d. Then we give the tighter bound of z which is a reflection of correction capability on d^z-disjunct matrix by the preceding result.