Synchronization of High-Dimensional Linear Networks over Finite Fields

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.