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Error-correcting nonadaptive group testing with d e -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 μ is called d e -disjunct if given any d + 1 columns of μ 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 d e -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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Applied Mathematics Elsevier
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