digital fingerprinting has been proposed to restrict illegal distribution of digital media, where every piece of media has a unique fingerprint as an identifying feature that can be traceable. however, fingerprint systems are vulnerable when multiple users form collusion by combining their copies to create a forged copy. the collusion is modeled as an average linear attack, where multiple weighted copies are averaged and the gaussian noise is then added to the averaged copy. in this thesis, a new fingerprint design with robustness to collusion is proposed, which is to accommodate more users and parameters than other existing fingerprint designs. a base matrix is constructed by cyclic shifts of binary sequences in an optical orthogonal code and then extended by a hadamard matrix. finally, each column of the resulting matrix is used as a fingerprint. the focused detection is used to determine whether a user is innocent or guilty in average linear attacks. simulation results show that the performance of our new fingerprint design is comparable to that of orthogonal and simplex fingerprints.