A (w,r) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A binary (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as a concept of key distribution patterns. In this paper, we develop a method of constructing superimposed codes and prove that some superimposed codes constructed in this way are optimal.
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Kim et al. (2003) studied this question.
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