Zongduo , Dai et al., Classification and Enumeration of Matched Free Response Matrices of d The Linear Finite Automata, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 13(1), 1997, pp. 133-144
If H and G are the transfer function matrix and the free response matrix of a linear finite automaton, then G is called a free response matrix matched to H. Given H, let G(H) be the set of all possible free response matrices matched to H. A classification and an enumeration on the set 9(H) are given in this paper.