Upper bounds on the size of quantum codes

This paper is concerned with bounds for quantum error-correcting codes, Usi ng the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this appr oach, we obtain Singleton-type, Hamming-type, and the first linear-programm ing-type bounds for quantum codes. Using the special structure of linear qu antum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.