On error-tolerant DNA screening

Given n clones with some positive ones, the problem of DNA screening is to identify all positive clones with a set of tests each on a subset of clones, called a pool and the outcome is either the pool contains a positive clone or not. In this paper, we show that for a class of designs, if we apply those for samples with d   positive clones to samples with at most d-1d-1 positive clones, the error-tolerant property will have an interesting improvement. We also make a remark on decoding method for k-error-correcting d-disjunct matrix.