Use Of The Finite Symplectic, Unitary Space, The Dual Space Of The Sub-space Structure For D ~ Z-disjunction Matrix

Recently non-adaptive group testing is developing actively,because it has many prac-tical applications.A d- disjunct matrix corresponds precisely to a pooling design which can identify at most d negative items using t tests from n items.Designing good error-tolerant pooling design is a central problem in the area of non-adaptive group testing. Macula firstly proposed that using d~z - disjunct matrix reflects the error-correction ca-pability of a d - disjunct matrix.In the present thesis,we introduce the history of group and preliminary knowledge on CGT firstly.Then we use subspaces in dual space of the Symplectic and Unitary space over finite fields construct d~z-disjunct matrices respectively.Finally we give their several properties and discuss the ratio n/t.