Title :
Upper bounds on the size of quantum codes
Author :
Ashikhmin, Alexei ; Litsyu, S.
Author_Institution :
Los Alamos Nat. Lab., NM, USA
fDate :
5/1/1999 12:00:00 AM
Abstract :
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
Keywords :
error correction codes; linear codes; linear programming; quantum cryptography; Hamming-type bound; Singleton-type bound; classical coding theory; code rates; code size; first linear programming bound; linear quantum codes; quantum MacWilliams identities; quantum error-correcting codes; upper bound; upper bounds; Application software; Computer errors; Error correction codes; Linear programming; Polynomials; Protection; Quantum computing; Quantum mechanics; Rain; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
