Quantum Codes and Abelian Subgroups of the Extra-Special Group
Problems of Information Transmission
On a problem concerning the quantum hamming bound for impure quantum codes
IEEE Transactions on Information Theory
Application of classical hermitian self-orthogonal MDS codes to quantum MDS codes
IEEE Transactions on Information Theory
Dualities and identities for entanglement-assisted quantum codes
Quantum Information Processing
| Hi-index | 754.96 |
This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams (1972, 1977) identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates