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.