Abstract As a generalization of de-disjunct matrices and (w,r;d)-cover-freefamilies, the notion of (s,l)e-disjunct matrices is introduced for error-correcting pooling designs over complexes (or set pooling designs). We show that (w,r,d)cover-free-families form a class of (s,l)e-disjunct matrices. Moreover, a decoding algorithm for pooling designs based on (s,l)e-disjunct matrices is considered. Keywords Pooling design · Disjunct matrix · Decoding · Complex