Digital fingerprinting is an effective technique to fight against the pirates of digital multimedia, which can trace users by embedding special information with distinct iden-tities into multimedia contents. Conventional fingerprinting techniques cannot resist collusion attack, where a coalition of different users with the same content try to disrupt the underlying fingerprints. AND anti-collusion codes (AND-ACC) were introduced by Trappe et al. to withstand collusion. Logical anti-collusion codes and separable codes, proposed by Cheng and Miao based on AND-ACC, also can resist collusion.The current researches on anti-collusion codes mainly focus on constructing an anti-collusion code or calculating the size of an anti-collusion code. With the basis of pioneers’work, first we study the properties and constructions of AND-ACC and provide a method to construct an AND-ACC by means of pairwise balanced designs (PBDs). According to the relations between separable codes and other mathematical structures, we then investigate the upper bound on the size of2-separable codes of length2and solve it when the size of alphabet q=16,25, in the view of combinatorial designs. In the end, we present a recursive construction for2-separable codes and get a lower bound on the size of2-separable codes. |