New construction of error-correcting pooling designs from singular linear spaces over finite fields

Abstract

The group testing problem is that we are asked to identify all the defects with the minimum number of tests when given a set of n items with at most d defects. In this paper, as a generalization of Liu et al.’s construction in the paper (Liu and Gao in Discret Math 338:857–862, 2015), new pooling designs are constructed from singular linear spaces over finite fields. Then we make comparisons with Liu et al.’s construction in the aspects of parameters of pooling designs. By choosing appropriate parameters in our pooling designs, the performance of test efficiency in our pooling designs is better than that given by Liu et al. Finally, the analysis of parameters in our pooling designs is provided.