  Given a completely positive map, we introduce a set of algebras that we refer
to as its generalized multiplicative domains. These algebras are
generalizations of the traditional multiplicative domain of a completely
positive map and we derive a characterization of them in the unital,
trace-preserving case, in other words the case of unital quantum channels, that
extends Choi's characterization of the multiplicative domains of unital maps.
We also derive a characterization that is in the same flavour as a well-known
characterization of bimodules, and we use these algebras to provide a new
representation-theoretic description of quantum error-correcting codes that
extends previous results for unitarily-correctable codes, noiseless subsystems
and decoherence-free subspaces.
