Quantum Codes from Constacyclic Codes over Polynomial Residue Rings

DING Jian; LI Hongju; LIANG Jing; TANG Yongsheng

doi:10.1049/cje.2019.07.007

Volume 28 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Electronics > 2019 > 28(6): 1131-1138

DING Jian, LI Hongju, LIANG Jing, et al., “Quantum Codes from Constacyclic Codes over Polynomial Residue Rings,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1131-1138, 2019, doi: 10.1049/cje.2019.07.007

Citation:

DING Jian, LI Hongju, LIANG Jing, et al., “Quantum Codes from Constacyclic Codes over Polynomial Residue Rings,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1131-1138, 2019, doi: 10.1049/cje.2019.07.007

Citation:

PDF( 475 KB)

Quantum Codes from Constacyclic Codes over Polynomial Residue Rings

doi: 10.1049/cje.2019.07.007

1.
College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China;
2.
Fujian Provincial Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou 350007, China;
3.
Department of General Education, Anhui Xinhua University, Hefei 230088, China;
4.
School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61572132), Natural Science Foundation of Anhui Province (No.1808085MA15), and Key University Science Research Project of Anhui Province (No.KJ2017A623, No.KJ2018A0584, No.KJ2018A0497).

Received Date: 2017-02-13
Rev Recd Date: 2017-10-30
Publish Date: 2019-11-10

Abstract

Abstract

Sufficient and necessary conditions for Hermitian (1+λu)-constacyclic self-orthogonal codes over F_p^m+uF_p^m are obtained, where λ is a unit of F_p^m+uF_p^m. Based on this, a new method for the construction of p^m-ary quantum codes from the obtained Hermitian (1+λu)-constacyclic self-orthogonal codes over F_p^m+uF_p^m is given. As an example,[[p^m-1, p_m-2d+1, d]]_p^m quantum MDS codes are constructed for 1 ≤ d ≤ (p^m+1)/2 and p≠2, as well as some other quantum codes.
- Quantum code,
- Quantum MDS code,
- Constacyclic code,
- Self-orthogonal code

FullText(HTML)

References(17)

References

P.W. Shor, "Scheme for reducing decoherence in quantum computer memory", Physical Review A, Vol.52, No.4, pp.2493-2496, 1995.

A.R. Calderbank, E.M. Rains, P.W. Shor, et al., "Quantum error correction via codes over GF(4)", IEEE Transactions on Information Theory, Vol.44, No.4, pp.1369-1387, 1998.

J. Qian, W. Ma and W. Guo, "Quantum codes from cyclic codes over finite ring", International Journal of Quantum Information, Vol.7, No.6, pp.1277-1283, 2009.

X. Yin and W. Ma, "Gray map and quantum codes over the ring F₂+uF₂+u²F₂", IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications, Changsha, China, pp.897-899, 2011.

X.S. Kai and S.X. Zhu, "Quaternary construction of quantum codes from cyclic codes over F₄+uF₄", International Journal of Quantum Information, Vol.9, No.2, pp.689-700, 2011.

Y.S. Tang, S.X. Zhu and X.S. Kai, "New quantum codes from dual-containing cyclic codes over finite rings", Quantum Information Processing, Vol.15, No.11, pp.4489-4500, 2016.

J. Li, "Quantum codes from cyclic codes over ring F_q+uF_q", Journal of University of Science and Technology of China, Vol.45, No.3, pp.199-204, 2015.

M. Ashraf and G. Mohammad, "Quantum codes from cyclic codes over F₃+vF₃", International Journal of Quantum Information, Vol.12, No.6, pp.1450042-1-1450042-8, 2014.

J. Gao, "Quantum codes from cyclic codes over F_q+vF_q+v²F_q+v³F_q", International Journal of Quantum Information, Vol.13, No.8, pp.1550063-1-1550063-8, 2015.

M. Ashraf and G. Mohammad, "Quantum codes from cyclic codes over F q+uF_q+vF_q+uvF_q", Quantum Information Processing, Vol.15, No.10, pp.4089-4098, 2016.

X. Liu and H. Liu, "Quantum codes from linear codes over finite chain rings", Quantum Information Processing, https://doi.org/10.1007/s11128-017-1695-7,2017.

X.S. Kai and S.X. Zhu, "New quantum MDS codes from negacyclic codes", IEEE Transactions on Information Theory, Vol.59, No.2, pp.1193-1197, 2013.

Y. Li and S.X. Zhu, "A class of constacyclic codes over the ring F_p^m+uF_p^m+…+u^k-1F_p^m", Journal of Hefei University of Technology, Vol.35, No.3, pp.408-411, 2013. (in Chinese)

J. Ding and H. Li, "Construction of optimal codes with Homogeneous distance", Journal of University of Science and Technology of China, Vol.45, No.7, pp.588-593, 2015.

G.G.L. Guardia, "On the Construction of non-binary quantum BCH codes", IEEE Transactions on Information Theory, Vol.60, No.3, pp.1528-1536, 2014.

M. Hamada, "Concatenated quantum codes constructible in polynomial time:Efficient decoding and error correction", IEEE Transactions on Information Theory, Vol.54, No.12, pp.5689-5704, 2008.

G.G.L. Giuliano and P.J. Reginaldo, "Constructions of new families of non-binary CSS codes", Discrete Mathematics, Vol.310, No.21, pp.2935-2945, 2010.

Relative Articles

Supplements(0)

Cited By

Proportional views