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Quantum Information Processing
Published in: Quantum Information Processing 3/2024

01-03-2024

Hermitian self-orthogonal matrix product codes and their applications to quantum codes

Author: Xiaoyan Zhang

Published in: Quantum Information Processing | Issue 3/2024

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Abstract

In this paper, we propose a construction of quantum codes from Hermitian self-orthogonal matrix product codes over the finite fields. This construction is applied to obtain numerous new quantum codes, and all of them have higher rate than current quantum codes available.
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Literature
1.
Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53(3), 1183–1188 (2007)MathSciNetCrossRef
2.
3.
Blackmore, T., Norton, G.H.: Matrix-product codes over \(\mathbb{F} _q\). Appl. Algebra Eng. Commun. Comput. 12, 477–500 (2001)CrossRef
4.
Bag, T., Dinh, H., Upadhyay, A., Bandi, R., Yamaka, W.: Quantum codes from skew constacyclic codes over the ring \(\mathbb{F} _q[u, v]/\langle u^2-1, v^2-1, uv-vu\rangle \). Discrete Math. 343, 111737 (2020)MathSciNetCrossRef
5.
Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over \(GF(4)\). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)MathSciNetCrossRef
6.
Cao, M., Wang, H., Cu, J.: Construction of quantum codes from matrix-product codes. IEEE Commun. Lett. 24(4), 706–710 (2020)CrossRef
7.
Cannon, J., Playoust, C.: An Introduction to Magma. The University of Sydney, Sydney (1994)
8.
Galindo, C., Hernando, F., Ruano, D.: New quantum codes from evaluation and matrix-product codes. Finite Fields Their Appl. 36, 98–120 (2015)MathSciNetCrossRef
9.
Jin, L., Ling, S., Luo, J., Xing, C.: Application of classical Hermitian self-orthogonal MDS codes to quantum MDS codes. IEEE Trans. Inf. Theory 56(9), 4735–4740 (2010)MathSciNetCrossRef
10.
11.
12.
Liu, X.S., Dinh, H.Q., Liu, H., Yu, L.: On new quantum codes from matrix product codes. Cryptogr. Commun. 10(4), 579–589 (2018)ADSMathSciNetCrossRef
13.
Liu, X.S., Yu, L., Hu, P.: New entanglement-assisted quantum codes from \(k\)-Galois dual codes. Finite Field Appl. 55, 21–32 (2019)MathSciNetCrossRef
14.
Ma, F., Cao, J.: New non-binary quantum codes from constacyclic codes over \(\mathbb{F} _q[u, v]/\langle u^2-1, v^2-v, uv-vu\rangle \). Adv. Math. Commun. 13(3), 421–434 (2019)MathSciNetCrossRef
15.
Steane, A.M.: Multiple-particle interference and quantum error correction. Phys. Proc. Math. Phys. Eng. Sci. 452(1954), 2551–2577 (1996)MathSciNetCrossRef
16.
17.
18.
Metadata
Title
Hermitian self-orthogonal matrix product codes and their applications to quantum codes
Author
Xiaoyan Zhang
Publication date
01-03-2024
Publisher
Springer US
Published in
Quantum Information Processing / Issue 3/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-024-04314-z

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