  By cross-matching the currently largest optical catalog of galaxy clusters
and the NVSS radio survey database, we obtain the largest complete sample of
brightest cluster galaxies (BCGs) in the redshift range of 0.05<z<0.45, which
have radio emission and redshift information. We confirm that more powerful
radio BCGs tend to be these optically very bight galaxies located in more
relaxed clusters. We derived the radio luminosity functions of BCGs from the
largest complete sample of BCGs, and find that the functions depend on the
optical luminosity of BCGs and the dynamical state of galaxy clusters. However,
the radio luminosity function does not show significant evolution with
redshift.
