Binary construction of quantum codes of minimum distance three and four

IEEE Transactions on Information Theory

Volumn 50, Issue 6, 2004, Pages 1331-1336

  Li, Ruihu ^a,b   Li, Xueliang ^c  

^a AIR FORCE ENGINEERING UNIVERSITY   (China)

^b NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^c NANKAI UNIVERSITY   (China)

Author keywords

Binary code; Quantum error correcting code; Self orthogonal code

Indexed keywords

BINARY CODES; DECODING; DISTANCE MEASUREMENT; THEOREM PROVING;

BINARY SELF ORTHOGONAL CODES; QUANTUM CODES;

QUANTUM EFFICIENCY;

EID: 2942640141     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.828149     Document Type: Letter

References (12)

1. J. Bierbrauer and Y. Edel, "Quantum twisted codes," J. Combin. Des., vol. 8, pp. 174-188, 2000.
2. 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.
3. A. R. Calderbank and P. W. Shor, "Good quantum error-correcting codes exist," Phys. Rev. A, vol. 54, pp. 1098-1105, Aug. 1996.
4. H. Chen, "Some good quantum error-correcting codes from algebric geometric codes," IEEE Trans. Inform. Theory, vol. 47, pp. 2059-2061, July 2001.
5. H. Chen, S. Ling, and C. P. Xing, "Quantum codes from concatenated algebric geometric codes," preprint, 2001.
6. D. Gottesman, "A class of quantum error-correcting codes saturating the quantum Hamming bound," Phys. Rev. A, vol. 54, pp. 1862-1868, 1996.
7. F. J. MacWillams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
8. P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A, vol. 52, pp. R2493-2496, Oct. 1995.
9. A. M. Steane, "Error correcting codes in quantum theory," Phys. Rev. Lett., vol. 77, pp. 793-797, July 1996.
10. ____, "Quantum Reed-Muller codes," IEEE Trans. Inform. Theory, vol. 45, pp. 1701-1703, July 1999.
11. ____, "Enlargement of Calderbank-Shor-Steane quantum codes," IEEE Trans. Inform. Theory, vol. 45, pp. 2492-2495, Nov. 1999.
12. V. Pless, "A classification of self-orthogonal codes over GF(2)," Discr. Math., vol. 3, pp. 209-246, 1972.