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Digital fingerprinting is an effective method to identify users who might try to redistribute multimedia content, such as images and video. These fingerprints are typically embedded into the content using watermarking techniques that are designed to be robust to a variety of attacks. A cheap and effective attack against such digital fingerprints is collusion, where several differently marked copies of the same content are averaged or combined to disrupt the underlying fingerprint. In this paper, we study the problem of designing fingerprints that can withstand collusion, yet trace colluders. Since, in antipodal CDMA-type watermarking, the correlation contributions only decrease where watermarks differ, by constructing binary code vectors where any subset of k or fewer of these vectors have unique overlap, we may identify groups of k or less colluders. Our construction of such anti-collusion codes (ACC) uses the theory of combinatorial designs, and for n users requires O(√n) bits. Further, we explore a block matrix structure for the ACC that reduces the computational complexity for identifying colluders and improves the detection capability when colluders belong to the same subgroup.