  Brightest Cluster Galaxies (BCGs) show exceptional properties over the whole
electromagnetic spectrum. Their special location at the centres of galaxy
clusters raises the question of the role of the environment on their radio
properties. To decouple the effect of the galaxy mass and of the environment in
their statistical radio properties, we investigate the possible dependence of
the occurrence of radio loudness and of the fractional radio luminosity
function on the dynamical state of the hosting cluster. We studied the radio
properties of the BCGs in the Extended GMRT Radio Halo Survey (EGRHS). We
obtained a statistical sample of 59 BCGs, which was divided into two classes,
depending on the dynamical state of the host cluster, i.e. merging (M) and
relaxed (R). Among the 59 BCGs, 28 are radio-loud, and 31 are radio--quiet. The
radio-loud sources are located favourably located in relaxed clusters (71\%),
while the reverse is true for the radio-quiet BCGs, mostly located in merging
systems (81\%). The fractional radio luminosity function (RLF) for the BCGs is
considerably higher for BCGs in relaxed clusters, where the total fraction of
radio loudness reaches almost 90\%, to be compared to the $\sim$30\% in merging
clusters. For relaxed clusters, we found a positive correlation between the
radio power of the BCGs and the strength of the cool core, consistent with
previous studies on local samples. Our study suggests that the radio loudness
of the BCGs strongly depends on the cluster dynamics, their fraction being
considerably higher in relaxed clusters. We compared our results with similar
investigations, and briefly discussed them in the framework of AGN feedback.
