Good digital fingerprinting codes

We construct binary t-secure fingerprinting codes (t=const) of size M=exp(cn), where n is the length of the fingerprint, for which the dealer (decoder) can recover at least one of the users from the colluding coalition with probability 1-exp(-f(c)n). For the case t=2 we construct codes with the property that the dealer can either recover both users of the coalition with probability 1-exp{(const)n}, or identifies one of them with probability 1.