Remark on the Uniqueness of $(w,r)$-Cover-Pree Codes

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 sets is not covered by the union of any other $r$ sets. For certain $(w,r)$ cover-free codes with a simple structure, we obtain a new condition of optimality and uniqueness up to row and/or column permutations.