  Given a dynamical system $(X,G)$, the centralizer $C(G)$ denotes the group of
all homeomorphisms of $X$ which commute with the action of $G$. This group is
sometimes called the automorphism group of the dynamical system $(X,G)$. In
this note, we generalize the construction of Bulatek and Kwiatkowski (1992) to
$\mathbb Z^d$-Toepltiz systems by identifying a class of $\mathbb Z^d$-Toeplitz
systems that have trivial centralizers. We show that this class of $\mathbb
Z^d$-Toeplitz with trivial centralizers contains systems with positive
topological entropy.
