New bounds on 2-frameproof codes of length 4 (Q1989034)

Summary: Frameproof codes were first introduced by \textit{D. Boneh} and \textit{J. Shaw} [IEEE Trans. Inf. Theory 44, No. 5, 1897--1905 (1998; Zbl 0931.94051)] in the context of digital fingerprinting to protect copyrighted materials. These digital fingerprints are generally denoted as codewords in \(Q^n\), where \(Q\) is an alphabet of size \(q\) and \(n\) is a positive integer. A 2-frameproof code is a code \(C\) such that any 2 codewords in \(C\) cannot form a new codeword under a particular rule. Thus, no pair of users can frame a user who is not a member of the coalition. This paper concentrates on the upper bound for the size of a \(q\)-ary 2-frameproof code of length 4. Our new upper bound shows that \(|C| \leq 2 q^2 -2q +1\) when \(q\) is odd and \(q > 10\).