Research PapersNo Access

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

RUIHU LI

School of Science, Air Force Engineering University, Xi'an, Shaanxi 710051, P. R. China

Search for more papers by this author

GEN XU

School of Science, Air Force Engineering University, Xi'an, Shaanxi 710051, P. R. China

Search for more papers by this author

, and

LUOBIN GUO

School of Science, Air Force Engineering University, Xi'an, Shaanxi 710051, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0217979214500179Cited by:9 (Source: Crossref)

Abstract

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]₂ asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]₂ exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with d_z> δ_max+1 from binary primitive cyclic codes of length n = 2^m-1, where δ_max = 2^⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2^m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

Keywords:

PACS: 03.67.Hk, 03.67.Lx

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

P. W. Shor, Phys. Rev. A 52, R2493 (1995), DOI: 10.1103/PhysRevA.52.R2493. Web of Science, ADS, Google Scholar
A. M. Steane, Phys. Rev. Lett. 77, 793 (1996), DOI: 10.1103/PhysRevLett.77.793. Web of Science, ADS, Google Scholar
A. R. Calderbanket al., IEEE. Trans. Inf. Theory 44, 1369 (1998), DOI: 10.1109/18.681315. Web of Science, Google Scholar
L. Ioffe and M. M. Mezard, Phys. Rev. A 75, 032345 (2007), DOI: 10.1103/PhysRevA.75.032345. Web of Science, Google Scholar
A. M. Steane, Phys. Rev. A 64, 4741 (1996). Google Scholar
S. A. Aly, PhD. Thesies, Texas A & M University, College Station, TX, 2008 . Google Scholar
S. A. Aly, International Conference on Computer Engineering and Systems, ICCES 2008 () pp. 157–162. Google Scholar
P. K. Sarvepalli, A. Klappenecker and M. Rotteler, Proc. R. Soc. A 465, 1645 (2009), DOI: 10.1098/rspa.2008.0439. ADS, Google Scholar
L. Wanget al., IEEE. Trans. Inf. Theory 56, 2938 (2010), DOI: 10.1109/TIT.2010.2046221. Web of Science, Google Scholar
M. F. Ezerman, S. Ling and P. Sole, IEEE. Trans. Inf. Theory 57, 5536 (2011), DOI: 10.1109/TIT.2011.2159040. Web of Science, Google Scholar
M. F. Ezerman, S. Jitman, S. Ling and D. V. Pasechnik, CSS-like construction of asymmetric quantum codes, , arXiv:1207.6512v1 [cs.IT] . Google Scholar
K. Guenda and T. A. Gulliver, New symmetric and asymmetric quantum codes, , arXiv:1207.3133v2 [cs.IT] . Google Scholar
G. G. La Guardia, Quantum Inf. Comput. 11, 0239 (2011). Web of Science, Google Scholar
G. G. La Guardia, Quantum Inf. Process 12, 2771 (2013), DOI: 10.1007/s11128-013-0562-4. Web of Science, ADS, Google Scholar
R. Leng and Z. Ma, Phys. Mech. Astronom. 55, 465 (2012), DOI: 10.1007/s11433-012-4655-3. Web of Science, Google Scholar
L. Guo and R. Li, On construction of binary asymmetric quantum codes of short length, ICISCE 2012, pp. 298–301 . Google Scholar
R. Liet al., Quant. Inf. Comput. 13, 0021 (2013). Web of Science, Google Scholar
A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 900 (1997). Web of Science, Google Scholar
A. M. Steane, IEEE Trans. Inf. Theory 45, 2492 (1999), DOI: 10.1109/18.796388. Web of Science, Google Scholar
K. Betsumiya and M. Harada, Desin. Codes Crypt. 23, 325 (2001), DOI: 10.1023/A:1011223128089. Web of Science, Google Scholar
A. Ketkar, A. Klappenecker and S. Kumar, IEEE. Trans. Inform. Theory 52, 4892 (2006), DOI: 10.1109/TIT.2006.883612. Web of Science, Google Scholar
W. C. Huffman and V. Pless , Fundamentals of Error-Correcting Codes ( Cambridge University Press , Cambridge , 2003 ) . Google Scholar
F. J. Macwilliams and N. J. A. Sloane , The Theory of Error-Correcting Codes ( North-Holland , Amsterdam , 1977 ) . Google Scholar
N. J. A. Sloane and J. G. Thompson, IEEE. Trans. Inf. Theory 29, 364 (1983), DOI: 10.1109/TIT.1983.1056682. Web of Science, Google Scholar
R. Li and X. Li, Int. J. Quantum Inf. 2, 265 (2004), DOI: 10.1142/S0219749904000213. Link, Web of Science, Google Scholar
D. Augot and F. Levy-dit-Vehel, IEEE Trans. Inf. Theory 42, 1257 (1996), DOI: 10.1109/18.508853. Web of Science, Google Scholar
P. Charpin, Handbook of Coding Theory II, eds. V. S. Pless and W. C. Huffman (Elsevier, Amsterdam, 1998) pp. 1345–1439. Google Scholar
C. Bracken and T. Helleseth, Proceedings of ISIT 2009 (2009) pp. 1723–1725, arXiv:0901.1827v1 [cs.IT]. Google Scholar