  We show that a synchronized coded system $X$ is intrinsically ergodic of full
support if and only if $ h(Y)$, the topological entropy of $Y$, is less than
$h(X) $ whenever $Y$ is a proper subsystem of $ X $. We also show that like
systems with specification property, SVGL's the non-mixing extension of systems
with specification property, are intrinsically ergodic of full support.
Moreover, we compute the entropy of the underlying graph of the Fischer cover
of a synchronized system.
