Construction Of Pooling Designs With Singular Linear Space And Singular Unitary Space

Group test originated in World War II in order to identify the blood samples containing the virus in all blood samples. According to different test procedures, it can be divided into timing algorithm and non-adaptive test algorithms. The basic model of the non-adaptive group testing design is a pooling design, and a mathematical model of a pooling design is a dz-disjunct matrix. Designing a good error-tolerant pooling design is the central problem in the area of non-adaptive group testing. The following works are presented based on the relative background of pooling design and the definitions of a dz-disjunct matrix:1. The construction from singular linear space.A family of error-correcting pooling designs with the incidence matrix of two types of subspaces of singular linear space over finite fields has been constructed, and their disjunct properties have been exhibited. Moreover, the new construction gives better ratio of efficiency than the former ones under conditions. At last, the paper gives the brief introduction about the relationship between the columns(rows) of the matrix and the related parameter by fixing the others.2. The construction from singular unitary space.Using the incidence matrix of two types of subspaces of singular unitary space over finite fields, we construct a family of error-correcting pooling designs and exhibit their disjunct properties. It shows the necessity of the new design to us by comparing the test efficiency t/s of the new design with the former ones. Finally, we know how the relative parameters influence the test efficiency by analyzing the relationship between the columns(rows) of the matrix and the related parameter.