  This paper investigates the synchronization problems for general
high-dimensional linear networks over finite fields. By using the technique of
linear transformations and invariant subspaces for linear spaces over finite
fields, several necessary and sufficient conditions for the synchronization of
high-dimensional linear networks over finite fields are proposed. This paper
not only generalizes the existing results from 1-dimensional to
high-dimensional linear networks but also adopts a new approach. Finally, some
numerical examples are given to illustrate the effectiveness of our theoretical
results.
