  We show that the multiplicative domain of a completely positive map yields a
new class of quantum error correcting codes. In the case of a unital quantum
channel, these are precisely the codes that do not require a measurement as
part of the recovery process, the so-called unitarily correctable codes.
Whereas in the arbitrary, not necessarily unital case they form a proper subset
of unitarily correctable codes that can be computed from properties of the
channel. As part of the analysis we derive a representation theoretic
characterization of subsystem codes. We also present a number of illustrative
examples.
