An Algorithm for Generating Feedback Functions of k-ary De Bruijn Sequences by Raising Stage

k homomorphic mappings from k-ary n-stage de Bruijn-Good graph onto k-ary(n-1)-stage de Bruijn-Good graph are defined.By using the homomorphic mappings,we prove a relational theorem between n-stage nonsingular feedback function f(x_1,x_2,…,x_n) and(n-1)-stage nonsingular feedback function g(x_1,x_2,…,x_(n-1)),whose state graph is D_a(G_f),and give an algorithm for generating k-ary feedback functions of n-stage de Bruijn sequences from those of(n-1)-stage de Bruijn sequences.In particular,when k=2 and a=0,by using the simplicity of mapping D over Z_2,we give an effictive algorithm for generating n-stage feedback functions of de Bruijn sequences from(n-2~r)-stage the feedback functions,where r is a nature number.