Search
This Journal
This Journal
Anywhere
Quick Search in Journals
Enter words / phrases / DOI / ISBN / keywords / authors / etc
Access type:Only show content I have full access toOnly show Open Access
Advanced Search
0 My Cart
Sign in
Institutional Access

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

Research PapersNo Access

NONBINARY QUANTUM CODES DERIVED FROM REPEATED-ROOT CYCLIC CODES

College of Science, Anhui University of Science and Technology, Huainan 232007, China

Search for more papers by this author

and

College of Science, Anhui University of Science and Technology, Huainan 232007, China

Search for more papers by this author

https://doi.org/10.1142/S021798491350053XCited by:6 (Source: Crossref)

Abstract

Many good quantum error-correcting codes were constructed from cyclic codes. However, it is a difficult problem to determine the true minimum distance of quantum cyclic codes for large length n. In this work, we construct nonbinary quantum cyclic codes and asymmetric quantum cyclic codes that are derived from repeated-root cyclic codes for an arbitrary length p^s, and determine the true minimum distance of all those codes. Some proposed quantum cyclic codes are optimal. Additionally, some proposed asymmetric quantum cyclic codes have better parameters than the ones available in the literature.

Keywords:

PACS: 03.67.Pp, 03.67.Hk, 03.67.Lx

References

P. W. Shor, Phys. Rev. A 52, 2493 (1995), DOI: 10.1103/PhysRevA.52.R2493. Crossref, Web of Science, ADS, Google Scholar
A. R. Calderbanket al., IEEE Trans. Inf. Theory 44, 1369 (1998), DOI: 10.1109/18.681315. Crossref, Web of Science, Google Scholar
A. Ketkaret al., IEEE Trans. Inf. Theory 52, 4892 (2006), DOI: 10.1109/TIT.2006.883612. Crossref, Web of Science, Google Scholar
K. Feng, S. Ling and C. Xing, IEEE Trans. Inf. Theory 52, 986 (2006). Crossref, Web of Science, Google Scholar
R. Li, Z. Xu and X. Li, IEEE Trans. Inf. Theory 50, 1331 (2004), DOI: 10.1109/TIT.2004.828149. Crossref, Web of Science, Google Scholar
R. Li and Z. Xu, Phys. Rev. A 82, 052316 (2010), DOI: 10.1103/PhysRevA.82.052316. Crossref, Web of Science, Google Scholar
G. G. La Guardia and R. Palazzo Jr., Discrete Math. 310, 2935 (2010), DOI: 10.1016/j.disc.2010.06.043. Crossref, Web of Science, Google Scholar
Z. Li, L. Xing and X. Wang, IEEE Trans. Inf. Theory 55, 3821 (2009), DOI: 10.1109/TIT.2009.2023715. Crossref, Web of Science, Google Scholar
V. D. Tonchev, Discrete Math. 309, 4697 (2009), DOI: 10.1016/j.disc.2008.05.036. Crossref, Web of Science, Google Scholar
Z. Zang, Opt. Commun. 285, 521 (2012), DOI: 10.1016/j.optcom.2011.11.023. Crossref, Web of Science, ADS, Google Scholar
Z. Zang and W. Yang, J. Appl. Phys. 109, 103106 (2011), DOI: 10.1063/1.3587358. Crossref, Web of Science, Google Scholar
Z. Zang and Y. Zhang, Appl. Opt. 51, 3424 (2012), DOI: 10.1364/AO.51.003424. Crossref, Web of Science, ADS, Google Scholar
Z. Zang and Y. Zhang, J. Mod. Opt. 59, 161 (2012), DOI: 10.1080/09500340.2011.622842. Crossref, Web of Science, ADS, Google Scholar
L. Ioffe and M. Mezard, Phys. Rev. A 75, 032345 (2007), DOI: 10.1103/PhysRevA.75.032345. Crossref, 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
M. F. Ezerman, S. Ling and P. Sole, IEEE Trans. Inf. Theory 57, 5536 (2011), DOI: 10.1109/TIT.2011.2159040. Crossref, Web of Science, Google Scholar
J. Qian and L. Zhang, Mod. Phys. Lett. B 27, 1350010 (2013), DOI: 10.1142/S0217984913500103. Link, Web of Science, Google Scholar
A. Thangaraj, IEEE Trans. Inf. Theory 47, 1176 (2001), DOI: 10.1109/18.915675. Crossref, Web of Science, Google Scholar
S. A. Aly, A. Klappenedker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007), DOI: 10.1109/TIT.2006.890730. Crossref, Web of Science, Google Scholar
M. Grassl, W. Geiselmonn and T. Beth, AAECC 13, 231 (1999). Google Scholar
X. Kai and S. Zhu, Int. J. Quantum Inf. 9, 689 (2011), DOI: 10.1142/S0219749911007757. Link, Web of Science, Google Scholar
G. G. La Guardia, Quantum Inf. Process. 11, 591 (2012), DOI: 10.1007/s11128-011-0269-3. Crossref, Web of Science, Google Scholar
H. Q. Dinh, Finite Fields and Their Applications 14, 22 (2008), DOI: 10.1016/j.ffa.2007.07.001. Crossref, Web of Science, Google Scholar
S. Ling, J. Luo and C. Xing, IEEE Trans. Inf. Theory 56, 4080 (2010), DOI: 10.1109/TIT.2010.2050828. Crossref, Web of Science, Google Scholar
P. K. Sarvepalli, M. Rotteler and A. Klappenecker, Proc. ISIT (2008) pp. 305–309. Google Scholar
S. A. Aly, Proc. Computer Engineering and Systems (2008) pp. 157–162. Google Scholar
S. A. Aly and A. Ashikhmin, IEEE Information Theory Workshop (2010) pp. 1–5. Google Scholar
L. Wanget al., IEEE Trans. Inf. Theory 56, 2938 (2010), DOI: 10.1109/TIT.2010.2046221. Crossref, Web of Science, Google Scholar
M. F. Ezerman and S. Ling, Adv. Math. Commun. 5, 41 (2011). Crossref, Web of Science, Google Scholar
G. G. La Guardia, Quantum Inf. Comput. 11, 0239 (2011). Web of Science, Google Scholar
K. Feng and Z. Ma, IEEE Trans. Inf. Theory 50, 3323 (2004), DOI: 10.1109/TIT.2004.838088. Crossref, Web of Science, Google Scholar
G. Chen and R. Li, Des. Codes Cryptogr. (2012), DOI:10.1007/s10623-012-9620-7. Google Scholar

Journal cover image

Vol. 27, No. 08

Metrics

Downloaded 73 times

History

Received 27 December 2012

Revised 15 January 2013

Accepted 18 January 2013

Published: 4 March 2013

Keywords