Quantum block and convolutional codes from self-orthogonal product codes

IEEE International Symposium on Information Theory - Proceedings

Volumn 2005-January, Issue , 2005, Pages

  Grassl, Markus ^a   Rötteler, Martin ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVOLUTION; ERROR CORRECTION; INVENTORY CONTROL; QUANTUM COMPUTERS; QUANTUM NOISE;

PRODUCT CODE; QUANTUM CODES; QUANTUM CONVOLUTIONAL CODES; QUANTUM ERROR CORRECTING CODES; SELF-ORTHOGONAL CODE; TAIL-BITING;

CONVOLUTIONAL CODES;

EID: 85114382768     PISSN: 21578095     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2005.1523493     Document Type: Conference Paper

References (15)

1. A. Ashikhmin and E. Knill, "Nonbinary quantum stabilizer codes," IEEE Transactions on Information Theory, vol. 47, no. 7, pp. 3065-3072, Nov. 2001, Preprint quant-ph/0005008.
2. R. E. Blahut, Theory and Practice of Error Control Codes. Reading: Addison-Wesley, 1983.
3. Algebraic Codes for Data Transmission. Cambridge: Cambridge University Press, 2003.
4. W. Bosma, J. J. Cannon, and C. Playoust, "The Magma Algebra System I: The User Language," Journal of Symbolic Computation, vol. 24, no. 3-4, pp. 235-266, 1997.
5. A. R. Calderbank and P. W. Shor, "Good quantum error-correcting codes exist," Physical Review A, vol. 54, no. 2, pp. 1098-1105, Aug. 1996, preprint quant-ph/9512032.
6. R. T. Chien and S. W. Ng, "Dual Product Codes for Correction of Multiple Low-Density Burst Errors," IEEE Transactions on Information Theory, vol. 19, no. 5, pp. 672-677, Sept. 1973.
7. A. C. A. de Almeida and R. Palazzo, Jr., "A Concatenated [(4, 1, 3)] Quantum Convolutional Code," in 2004 IEEE Information Theory Workshop, San Antonio, TX, Oct. 2004.
8. G. D. Forney, Jr. and S. Guha, "Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes," Jan. 2005, preprint quantph/0501099.
9. M. Grassl and T. Beth, "Cyclic quantum error-correcting codes and quantum shift registers," Proceedings of the Royal Society London A, vol. 456, no. 2003, pp. 2689-2706, Nov. 2000, preprint quant-ph/9910061.
10. M. Grassl, T. Beth, and M. Rötteler, "On Optimal Quantum Codes," International Journal of Quantum Information, vol. 2, no. 1, pp. 55-64, 2004, preprint quant-ph/0312164.
11. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam: North-Holland, 1977.
12. H. Ollivier and J.-P. Tillich, "Description of a quantum convolutional code," Physical Review Letters, vol. 91, 177902, Oct. 24 2003.
13. -, "Quantum convolutional codes: Fundamentals," Nov. 2004, preprint quant-ph/0401134.
14. A. M. Steane, "Error Correcting Codes in Quantum Theory," Physical Review Letters, vol. 77, no. 5, pp. 793-797, 29. July 1996.
15. J. K. Wolf, "On Codes Derivable from the Tensor Product of Check Matrices," IEEE Transactions on Information Theory, vol. 11, no. 2, pp. 281-284, Apr. 1965.