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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
引用本文:张更生,曹晓艳.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[J].数学学报,2012(3):385-404.
作者姓名:张更生  曹晓艳
作者单位:河北师范大学数学与信息科学学院;河北省数学研究中心
基金项目:河北省自然科学基金资助项目(A2009000253)
摘    要: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.

关 键 词:Pooling设计  d~z-析取矩阵  酉空间

Arrangement Problem on the Subspace of the Unitary Space and d~z -Disjunct Matrix with Correction Capability
Geng Sheng ZHANG College of Mathematics and Information Science, Hebei Normal University,Shijiazhuang,P.R.China Hebei Center for Mathematics Research,Shijiazhuang,P.R.China Xiao Yan CAO.Arrangement Problem on the Subspace of the Unitary Space and d~z -Disjunct Matrix with Correction Capability[J].Acta Mathematica Sinica,2012(3):385-404.
Authors:Geng Sheng ZHANG College of Mathematics and Information Science  Hebei Normal University  Shijiazhuang  PRChina Hebei Center for Mathematics Research  Shijiazhuang  PRChina Xiao Yan CAO
Institution:College of Mathematics and Information Science, Hebei Normal University,Shijiazhuang 050016,P.R.China
Abstract:The pooling design has many application in practice.A mathematical model of pooling design is a dz-disjunct matrix.In this paper,we construct a kind of new dz-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 Fq2(n) and an integer d,we find d subspaces of type(m-1,s-1),H1,H2,...,Hd of C that maximize the number of the subspaces of type(r,s - 4) contained in H-1 U H2 U…U Hd. Then we give the tighter bound of z which is a reflection of correction capability on dz-disjunct matrix by the preceding result.
Keywords:pooling design  d~z-disjunct matrix  unitary space
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