On tight bounds for binary frameproof codes.

In this paper, we study $$w$$ -frameproof codes, which are equivalent to $$\{1,w\}$$ -separating hash families. Our main results concern binary codes, which are defined over an alphabet of two symbols. For all $$w \ge 3$$ , and for $$w+1 \le N \le 3w$$ , we show that an $${\mathsf {SHF}}(N; n,2, \{1,w \})$$ exists only if $$n \le N$$ , and an $${\mathsf {SHF}}(N; N,2, \{1,w \})$$ must be a permutation matrix of degree $$N$$ . [ABSTRACT FROM AUTHOR]