Nonbinary quantum codes

IEEE Transactions on Information Theory

Volumn 45, Issue 6, 1999, Pages 1827-1832

  Rains, Eric M ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

Finite fields; Quantum codes; Symplectic

Indexed keywords

ERROR CORRECTION; FAULT TOLERANT COMPUTER SYSTEMS; INVARIANCE; SIGNAL ENCODING; VECTORS;

FINITE FIELDS; NONBINARY QUANTUM CODES; SYMPLECTIC;

CODES (SYMBOLS);

EID: 0033184975     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.782103     Document Type: Article

References (13)

1. C. Bachoc, "Applications of coding theory to the construction of modular lattices," J. Combin. Theory Ser. A, vol. 78, pp. 92-119, 1997.
2. A. R. Calderbank, P. J. Cameron, W. M. Kantor, and J. J. Seidel, "ℤ4-Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets," Proc. London Math. Soc., vol. 75, pp. 436-480, 1997.
3. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, "Quantum error correction via codes over GF(4)," IEEE Trans. Inform. Theory, vol. 44, pp. 1369-1387, July 1998, LANL e-print quantph/9608006.
4. A. R. Calderbank and P. W. Shor, "Good quantum error-correcting codes exist," Phys. Rev. A. vol. 54, pp. 1098-1105, 1996, LANL e-print quant-ph/9512032.
5. P. Gaborit, "Mass formulas for self-dual codes over Z4 and F? + uF? rings," IEEE Trans. Inform. Theory, vol. 42, pp. 1222-1228, 1996.
6. D. Gottesman, "A theory of fault-tolerant quantum computation," Phys. Rev. A, vol. 57, no. 1, pp. 127-137, 1998, LANL e-print quantph/9702029.
7. "Fault-tolerant quantum computation with higher-dimensional systems," LANL e-print quant-ph/9802007.
8. E. Knill, "Non-binary error bases and quantum codes," LANL e-print quant-ph/9608048.
9. "Group representations, error bases and quantum codes," LANL e-print quant-ph/9608049.
10. E. Knill and R. Laflamme, "A theory of quantum error correcting codes," Phys. Rev. A, vol. 55, pp. 900-911, 1997, LANL e-print quantph/9604034.
11. E. M. Rains, "Quantum weight enumerators," IEEE Trans. Inform. Theory, vol. 44, pp. 1388-1394, July 1998, LANL e-print quantph/9612015.
12. A. Steane, "Simple quantum error correcting codes," Phys. Rev. Lett., vol. 77, pp. 793-797, 1996, LANL e-print quant-ph/9605021.
13. A. Weil, "Sur certaines groupes d'opérateurs unitaires," Acta. Arithm., vol. 11, pp. 143-211, 1964.