New Error-Correcting Pooling Designs with Singular Linear Spaces

Abstract

As a generalization of attenuated space, the concept of singular linear spaces was firstly introduced in [1]. In this paper, we construct a family of error-correcting pooling designs with the incidence matrix of two types of subspaces of singular linear space over finite fields, and exhibit their disjunct properties. Moreover, we show that the new construction gives better ratio of efficiency than the former ones under certain conditions. Finally, the paper gives a brief introduction about the relationship between the columns (rows) of the matrix and the related parameters.