Families of finite sets in which no intersection of \(\ell\) sets is covered by the union of \(s\) others (Q696905)

The authors generalize the concept of a superimposed code of strength \(s\) to a binary superimposed \((s,\ell)\)-code. It is determined by the incidence matrix of a family of finite sets in which no intersection of \(\ell\) sets is covered by the union of \(s\) others. The authors generalize also the concatenated construction of superimposed codes based on MDS-codes. Some bounds on the rate of the new codes are also presented in the paper.