  We show that within any quantum stabilizer code there lurks a classical
binary linear code with similar error-correcting capabilities, thereby
demonstrating new connections between quantum codes and classical codes. Using
this result -- which applies to degenerate as well as nondegenerate codes --
previously established necessary conditions for classical linear codes can be
easily translated into necessary conditions for quantum stabilizer codes.
Examples of specific consequences are: for a quantum channel subject to a
delta-fraction of errors, the best asymptotic capacity attainable by any
stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the
depolarizing channel with fidelity parameter delta, the best asymptotic
capacity attainable by any stabilizer code cannot exceed 1-H(delta).
