  There is an advantage in simultaneously transmitting both classical and
quantum information over a quantum channel compared to sending independent
transmissions. The successful implementation of simultaneous transmissions of
quantum and classical information will require the development of hybrid
quantum-classical error-correcting codes, known as hybrid codes. The
characterization of hybrid codes has been performed from a coding theory
perspective and an operator algebra quantum error correction (OAQEC)
perspective. First, we demonstrate that these two perspectives are equivalent
and that the coding theory characterization is a specific case of the OAQEC
model. Second, we include a generalization of the quantum Hamming bound for
hybrid error-correcting codes. We discover a necessary condition for developing
non-trivial hybrid codes -- they must be degenerate. Finally, we construct an
example of a non-trivial degenerate 4-qubit hybrid code.
