  Given a factor code between sofic shifts X and Y, there is a family of
decompositions of the original code into factor codes such that the entropies
of the intermediate subshifts arising from the decompositions are dense in the
interval from the entropy of Y to that of X. Furthermore, if X is of finite
type, we can choose those intermediate subshifts as shifts of finite type. In
the second part of the paper, given an embedding from a shift space to an
irreducible sofic shift, we characterize the set of the entropies of the
intermediate subshifts arising from the decompositions of the given embedding
into embeddings.
