Two applications of separating systems to nonadaptive procedures

Let [n] denote {1, 2, …, n}. A set system σ on [n] is called a separating system on [n] if for each pair of distinct elements in [n], there is an M ∈ σ that contains exactly one member of that pair. A separating system τ on [n] is called totally separating if for each pair of distinct elements j, j′ in [n], there are disjoint M, M′ ∈ τ with j ϵ M and j′ ∈ M′. In this paper, we discuss two applications of separating systems. In the first application, we give an easy method of constructing a class of single error-correcting double error-detecting codes over an Abelian group alphabet. In the second application, we construct a class of 3-separable matrices. Separable matrices are important notions in the theories of nonadaptive group testing and binary superimposed codes.