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A fingerprinting code is a set of codewords that are embedded in each copy of a digital object with the purpose of making each copy unique. If the fingerprinting code is c-secure with error, then the decoding of a pirate word created by a coalition of at most c dishonest users, will expose at least one of the guilty parties with probability 1-ϵ. The Boneh-Shaw fingerprinting codes are n-secure codes with ϵB error, where n also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order O(n3 log(n/ϵB)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (c<; n)-secure for lengths of order O(nc2 log(n/ϵB)). Moreover, in this paper it is also shown how to use these codes to construct binary fingerprinting codes of length L=O(c6 log(c/ϵ) log n), with probability of error ϵ<;ϵB and an identification algorithm of complexity poly(log n)=poly(L). These results improve in some aspects the best known schemes and with a much more simple construction.