Abstract
A binary code is called a (w, r) cover-free code if it is the incidence matrix of a family of sets where the intersection of any w of the sets is not covered by the union of any other r sets. Such a family is called a (w, r) cover-free family. We obtain a new recurrent inequality for the rate of (w, r) cover-free codes, which improves previously known upper bounds on the rate.
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