  Given a positive integer $M$ and $q \in (1, M+1]$ we consider expansions in
base $q$ for real numbers $x \in \left[0, {M}/{q-1}\right]$ over the alphabet
$\{0, \ldots, M\}$. In particular, we study some dynamical properties of the
natural occurring subshift $(\mathbf{V}_q, \sigma)$ related to unique
expansions in such base $q$. We characterise the set of $q \in (1,M+1]$ such
that $(\mathbf{V}_q, \sigma)$ has the specification property and the set of $q
\in (1,M+1]$ such that $(\mathbf{V}_q, \sigma)$ is a synchronised subshift.
Such properties are studied by analysing the combinatorial and dynamical
properties of the quasi-greedy expansion of $q$. We also calculate the size of
such classes giving similar results to those shown by Schmeling in (Ergodic
Theory and Dynamical Systems, 17:675--694, 6 1997) in the context of
$\beta$-transformations.
