Primitive quantum BCH codes over finite fields

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2006, Pages 1114-1118

  Aly, Salah A ^a   Klappenecker, Andreas ^a   Sarvepalli, Pradeep Kiran ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DESIGN PARAMETERS; FINITE FIELDS; HERMITIAN DUAL CODES; PRIMITIVE QUANTUM BCH CODES;

INFORMATION ANALYSIS; PARAMETER ESTIMATION; QUANTUM THEORY;

CONVOLUTIONAL CODES;

EID: 39049084399     PISSN: 21578101     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2006.261957     Document Type: Conference Paper

References (16)

1. A. Ashikhmin and E. Knill, "Nonbinary quantum stabilizer codes," IEEE Trans. Inform. Theory, vol. 47, no. 7, pp. 3065-3072, 2001.
2. J. Bierbrauer and Y. Edel, "Quantum twisted codes," J. Comb. Designs, vol. 8, no. 3, pp. 174-188, 2000.
3. A. Calderbank, E. Rains, P. Shor, and N. Sloane, "Quantum error correction via codes over GF(4)," IEEE Trans. Inform. Theory, vol. 44, pp. 1369-1387, 1998.
4. P. Charpin, "Open problems on cyclic codes," in Handbook of coding theory, Vol. I, II. Amsterdam: North-Holland, 1998, pp. 963-1063.
5. G. Cohen, S. Encheva, and S. Litsyn, "On binary constructions of quantum codes," IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2495-2498, 1999.
6. M. Grassl and T. Beth, "Quantum BCH codes," in Proc. X. Int'l. Symp. Theoretical Electrical Engineering, Magdeburg, 1999, pp. 207-212.
7. M. Grassl, T. Beth, and T. Pellizzari, "Codes for the quantum erasure channel," Phys. Rev. Lett. A, vol. 56, no. 1, pp. 33-38, 1997.
8. M. Grassl, T. Beth, and M. Rötteler, "On optimal quantum codes," Internat. J. Quantum Information, vol. 2, no. 1, pp. 757-775, 2004.
9. M. Grassl and T. Beth, "Cyclic quantum error-correcting codes and quantum shift registers," Proc. Royal Soc. London Series A, vol. 456, no. 2003, pp. 2689-2706, 2000.
10. W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes. Cambridge: University Press, 2003.
11. G. Kabatiansky, E. Krouk, and S. Semenov, Error Correcting Codes and Security for Data Networks. John Wiley, 2005.
12. F. Mac Williams and N. Sloane, The Theory of Error-Correcting Codes. North-Holland, 1977.
13. A. Steane, "Enlargement of Calderbank-Shor-Steane codes," IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2492-2495, 1999.
14. _, "Simple quantum error correcting codes," Phys. Rev. Lett., vol. 77, pp. 793-797, 1996.
15. H. Stichtenoth, "On the dimension of subfield subcodes," IEEE Trans. Inform. Theory, vol. 36, no. 1, pp. 90-93, 1990.
16. D.-W Yue and Z.-M. Hu, "On the dimension and minimum distance of BCH codes over GF(q)," J. Electron., vol. 18, pp. 263-269, 1996, (In Chinese).