  This paper presents a method to find new De Bruijn cycles based on ones of
lesser order. This is done by mapping a De Bruijn cycle to several vertex
disjoint cycles in a De Bruijn digraph of higher order and connecting these
cycles into one full cycle. We characterize homomorphisms between De Bruijn
digraphs of different orders that allow this construction. These maps
generalize the well-known D-morphism of Lempel between De Bruijn digraphs of
consecutive orders. Also, an efficient recursive algorithm that yields an
exponential number of nonbinary De Bruijn cycles is implemented.
