Error-correcting nonadaptive group testing with de-disjunct matrices

d-disjunct matrices constitute a basis for nonadaptive group testing (NGT) algorithms and binary d-superimposed codes. The rows of a d-disjunct matrix represent the tests in a NGT algorithm which identifies up to d defects in a population. The columns of a d-disjunct matrix represent binary d-superimposable codewords. A d-disjunct matrix mu is called d(e)-disjunct if given any d + 1 columns of mu with one designated, there are e + 1 rows with a 1 in the designated column and a 0 in each of the other d columns. d(e)-disjunct matrices form a basis for e error-correcting NGT algorithms. In this paper, we construct de-disjunct matrices. In so doing, we simultaneously construct e error-correcting binary d-superimposed codes. The results of this paper can be used to construct pooling designs for the screening recombinant DNA libraries. Such screenings are a major component of the Human Genome Project.