Abstract
Frameproof codes are used to fingerprint digital data. They can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for $w$ -frameproof codes of length $N$ over an alphabet of size $q$ . The upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction. Both bounds can improve one of the previous results when $q$ is small compared with $w$ , say $cq\leq w$ for some constant $c\leq q$ . Furthermore, we pay special attention to binary frameproof codes. We show a binary $w$ -frameproof code of length $N$ cannot have more than $N$ codewords if $N .
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