Quantum stabilizer codes and classical linear codes

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities. 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 as follows: for a quantum channel subject to a delta fraction of errors, the best asymptotic capacity attainable by ally stabilizer code cannot exceed H(1/2+root 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).