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Construction of nonbinary quantum cyclic codes by using graph method

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Abstract

Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8,2,4]] p and [[n,n − 2,2]] p for all odd primesp by the graph method.

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References

  1. Wootters, W. K., Zurek, W. H., A single quantum cannot be cloned, Nature, 1982, 299: 802–803.

    Article  Google Scholar 

  2. Shor, P. W., Scheme for reducing decoherence in quantum memory, Phys. Rev. A, 1995, 52: 2493.

    Article  Google Scholar 

  3. Steane, A. M., Multiple particle interference and quantum error correction, Proc. Roy. Soc. London A, 1996, 452: 2551–2557.

    MathSciNet  Google Scholar 

  4. Calderbank, A. R., Rains, E. M., Shor, P. W. et al., Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, 1998, 44(7): 1369–1387.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ashikhim, A., Knill, E., Non-binary quantum stabilizer codes, IEEE Trans. Inform. Theory, 2001, 47(11): 3065–3072.

    Article  MathSciNet  Google Scholar 

  6. Matsumoto, R., Uyematsu, T., Constructing quantum error-correcting codes forp m-state systems from classical error-correcting codes, 1999, quant-ph/9911011.

  7. Rains, E. M., Nonbinary quantum codes, IEEE Trans. Inform. Theory, 1999, 45(9): 1827–1832.

    Article  MATH  MathSciNet  Google Scholar 

  8. Schlingemann, D., Werner, R. F., Quantum error-correcting codes associated with graphs, Phys. Rev. A, 2001, 65: No. 012308. quant-ph/0012111.

  9. Feng, K. Q., Quantum Codes [[6,2,3]] p and [[7,3,3]] p (p ≥ 3) Exist, IEEE Trans. Inform. Theory, 2002, 48(8): 2384–2391.

    Article  MATH  MathSciNet  Google Scholar 

  10. Knill, E., Laflamme, R., A theory of quantum error-correcting codes, Phys. Rev. A, 1997, 55: 900–911.

    Article  MathSciNet  Google Scholar 

  11. Grassl, M., Klappenecker, A., Rötteler, M., Graphs, quadratic forms, and quantum codes, in Proc. IEEE Int. Symp. Information Theory, Lausanne, Switzerland, June/July 2002, 45.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

    Liu Tailin & Wen Qiaoyan

  2. State Key Laboratory of Integrated Services Network, Xidian University, 710071, Xi’an, China

    Liu Tailin

  3. Shandong Finance Institute, 250014, Jinan, China

    Liu Tailin

  4. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Liu Zihui

Authors
  1. Liu Tailin
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  2. Wen Qiaoyan
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  3. Liu Zihui
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Correspondence to Liu Tailin.

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Liu, T., Wen, Q. & Liu, Z. Construction of nonbinary quantum cyclic codes by using graph method. Sci China Ser F 48, 693–702 (2005). https://doi.org/10.1360/04yf0368

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  • DOI: https://doi.org/10.1360/04yf0368

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