On tight bounds for binary frameproof codes

Abstract

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 $SHF(N;n,2,\{1,w\})$ exists only if $n\le N$, and an $SHF(N;N,2,\{1,w\})$ must be a permutation matrix of degree $N$.