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Quantum Information Processing
Published in: Quantum Information Processing 10/2018

01-10-2018

Entanglement-assisted quantum MDS codes constructed from constacyclic codes

Authors: Xiaojing Chen, Shixin Zhu, Xiaoshan Kai

Published in: Quantum Information Processing | Issue 10/2018

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Abstract

Recently, entanglement-assisted quantum error-correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by decomposing the defining set of constacyclic codes, we construct four classes of new EAQECCs, which satisfy the entanglement-assisted quantum Singleton bound.
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Literature
1.
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), 2493–2496 (1995)ADSCrossRef
2.
3.
4.
Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over \(\rm GF(4)\). IEEE Trans. Inf. Theory 44(4), 1369–1387 (1998)MathSciNetCrossRef
5.
Grassl, M., Beth, T., Rtteler, M.: On optimal quantum codes. Int. J. Quantum Inf. 2(1), 55–64 (2004)CrossRef
6.
Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52(11), 4892–4914 (2006)MathSciNetCrossRef
7.
La Guardia, G.G.: Constructions of new families of nonbinary quantum codes. Phys. Rev. A 80(042331), 1–11 (2009)
8.
Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53(3), 1183–1188 (2007)MathSciNetCrossRef
9.
10.
Wilde, M.M., Brun, T.A.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A 77(064302), 1–4 (2008)
11.
Lai, C.-Y., Brun, T.A.: Entanglement increases the error-correcting ability of quantum error-correcting codes. Phys. Rev. A 88(012320), 1–10 (2013)
12.
Lu, L., Li, R., Guo, L., Fu, Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quantum Inf. Process. 14, 165–182 (2015)ADSMathSciNetCrossRef
13.
Brun, T.A., Devetak, I., Hsieh, M.-H.: Catalytic quantum error correction. IEEE Trans. Inf. Theory 60(6), 3073–3089 (2014)MathSciNetCrossRef
14.
Grassl, M.: Entanglement-Assisted Quantum Communication Beating the Quantum Singleton Bound. AQIS, Taipei (2016)
15.
Qian, J., Zhang, L.: On MDS linear complementary dual codes and entanglement-assisted quantum codes. Des. Codes Cryptogr. 86, 1565–1572 (2018)MathSciNetCrossRef
16.
Guenda, K., Jitman, S., Gulliver, T.A.: Constructions of good entanglement-assisted quanutm error correcting codes. Des. Codes Cryptogr. 86, 121–136 (2018)MathSciNetCrossRef
17.
Li, R., Zuo, F., Liu, Y.: A study of skew symmetric \(q^2\)-cyclotomic coset and its application. J. Air Force Eng. Univ. (Nat. Sci. Ed.) 12(1), 87–89 (2011). (in Chinese)
18.
Li, R., Xu, G., Lu, L.: Decomposition of defining sets of BCH codes and its applications. J. Air Force Eng. Univ. (Nat. Sci. Ed.) 14(2), 86–89 (2013). (in Chinese)
19.
Lü, L., Li, R.: Entanglement-assisted quantum codes constructed from primitive quaternary BCH codes. Int. J. Quantum Inf. 12(3), 14500151–145001514 (2014)MathSciNetCrossRef
20.
Chen, J., Huang, Y., Feng, C., Chen, R.: Entanglement-assisted quantum MDS codes constructed from negacyclic codes. Quantum Inf. Process. 16(303), 1–22 (2017)ADSMathSciNetMATH
21.
Lu, L., Li, R., Guo, L., Ma, Y., Liu, Y.: Entanglement-assisted quantum MDS codes from negacyclic codes. Quantum Inf. Process. 17(69), 1–23 (2018)ADSMathSciNetMATH
22.
Kai, X., Zhu, S., Li, P.: Constacyclic codes and some new quantum MDS codes. IEEE Trans. Inf. Theory 60(4), 2080–2086 (2014)MathSciNetCrossRef
23.
Zhang, T., Ge, G.: Some new classes of quantum MDS codes from constacyclic codes. IEEE Trans. Inf. Theory 61(9), 5224–5228 (2015)ADSMathSciNetCrossRef
24.
Chen, X., Zhu, S., Kai, X.: Two classes of new optimal asymmetric quantum codes. Int. J. Theor. Phys. 57(6), 1829–1838 (2018)MathSciNetCrossRef
25.
Aydin, N., Siap, I., Ray-Chaudhuri, D.K.: The structure of 1-generator quasi-twisted codes and new linear codes. Des. Codes Cryptogr. 24, 313–326 (2001)MathSciNetCrossRef
26.
Krishna, A., Sarwate, D.V.: Pseudocyclic maximum-distance-separable codes. IEEE Trans. Inf. Theory 36(4), 880–884 (1990)MathSciNetCrossRef
27.
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1997)MATH
Metadata
Title
Entanglement-assisted quantum MDS codes constructed from constacyclic codes
Authors
Xiaojing Chen
Shixin Zhu
Xiaoshan Kai
Publication date
01-10-2018
Publisher
Springer US
Published in
Quantum Information Processing / Issue 10/2018
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-018-2044-1

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