K-System Generator of Pseudorandom Numbers on Galois Field

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of the trajectories increases as a function of the lattice size p and the dimension of the K-matrixd. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.