  We consider the embedding problem in coding theory: given an independence (a
code-related property) and an independent language $L$, find a maximal
independent language containing $L$. We consider the case where the
code-related property is defined via a rational binary relation that is
decreasing with respect to any fixed total order on the set of words. Our
method works by iterating a max-min operator that has been used before for the
embedding problem for properties defined by length-increasing-and-transitive
binary relations. By going to order-decreasing rational relations, represented
by input-decreasing transducers, we are able to include many known properties
from both the noiseless and noisy domains of coding theory, as well as any
combination of such properties. Moreover, in many cases the desired maximal
embedding is effectively computable.
