We consider the ensembles of binary equal-weight fingerprinting codes de-
signed under the marking assumption. A random coding argument is used in
conjunction with a new decoding algorithm. The result is the new lower bounds
on the capacity Ct of fingerprinting codes that can identify at least one of t
pirates. In particular, for large t; we design long equal-weight fingerprinting
codes of the rate t^(-2) ln 2: