酉空间上一类析取矩阵的构造及紧界分析  

Constructing disjunction matrices with unitary space and analyzing the tighter bound

作　　者：张丽华[1] 牛美芳 ZHANG Lihua;NIU Meifang(School of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China)

机构地区：[1]沈阳师范大学数学与系统科学学院

出　　处：《沈阳师范大学学报（自然科学版）》2019年第3期250-253,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：高等学校大学数学教学研究与发展中心2019年教改项目(CMC20190502);辽宁省科技人员厅自然科学基金资助项目(20180550996)

摘　　要：析取矩阵主要用来检测样本空间中的阳性样本,也称为问题样本,而且每个析取矩阵都是一个(0,1)矩阵。目前有许多文献利用有限域上的几何空间(简称有限几何空间)来构作dz-析取矩阵,其中辛空间中的结果较多。在这些文献中,有一些是利用有限几何空间中的子空间之间的包含关系来构作dz-析取矩阵的,并且讨论了试验效率(dz-析取矩阵的行数与列数之比)及z的紧界。用酉空间F(n)q2的(m,s)-型子空间标识dz-析取矩阵的行,(r,s-1)-型子空间标识dz-析取矩阵的列,利用它们之间的包含关系构作了一类新的dz-析取矩阵。通过求包含在一个(m,s)-型子空间中的、d个(m-1,s-1)-型子空间里的、(r,s-1)-型子空间个数的最大值,给出了d和z的取值范围及z的紧界。由于(r,s-1)-型子空间中的s-1与(m,s)-型子空间中的s相差较小,所以本文能够相对较快地得到了d和z的的取值范围及z的紧界。Disjunction matrices mainly are used to test positive samples in sample space, which are also known as the problem samples, and every disjunction matrix is a (0,1) matrix.At present, many literatures make use of geometric spaces over a finite field to construct d z -disjunction matrices, in which there are more results in Symplectic Space.Some of these literatures make use of the inclusion relation between subspaces in geometric spaces over a finite field to construct d z -disjunction matrices, the test ratio (the ratio of the rows to columns of the d z -disjunction matrices) and the tighter bound of z are discussed.This paper uses the subspaces of the type of (m,s) in Unitary Space F (n) q2 to index the rows of the d z -disjunction matrices, the subspaces of the type of ( r,s-1 ) in Unitary Space F (n) q2 to index the columns of the d z -disjunction matrices, using the inclusion relation between them to construct a new class of d z -disjunction matrices.By means of calculating the largest number of the subspaces of the type of ( r,s-1 ) included in d subspaces of the type of ( m-1,s-1 ), which included in a given subspace of the type of ( m,s ), we give the value range of d and z and the tighter bound of z .Since the gap between s -1 in the subspaces of the type of ( r,s -1) and s in the subspaces of the type of ( m,s ) is smaller, the value range of d and z and the tighter bound of z can be relatively quick obtained in this paper.

关 键 词：POOLING设计 dz-析取矩阵 酉空间 紧界 

分 类 号：O157.2[理学—数学]