  We define and investigate a notion of entropy for quantum error correcting
codes. The entropy of a code for a given quantum channel has a number of
equivalent realisations, such as through the coefficients associated with the
Knill-Laflamme conditions and the entropy exchange computed with respect to any
initial state supported on the code. In general the entropy of a code can be
viewed as a measure of how close it is to the minimal entropy case, which is
given by unitarily correctable codes (including decoherence-free subspaces), or
the maximal entropy case, which from dynamical Choi matrix considerations
corresponds to non-degenerate codes. We consider several examples, including a
detailed analysis in the case of binary unitary channels, and we discuss an
extension of the entropy to operator quantum error correcting subsystem codes.
