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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Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53(3), 1183–1188 (2007)
Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Trans. Inf. Theory 47(7), 3065–3072 (2001)
Blackmore, T., Norton, G.H.: Matrix-product codes over \(\mathbb{F} _q\). Appl. Algebra Eng. Commun. Comput. 12, 477–500 (2001)
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)
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)
Cao, M., Wang, H., Cu, J.: Construction of quantum codes from matrix-product codes. IEEE Commun. Lett. 24(4), 706–710 (2020)
Cannon, J., Playoust, C.: An Introduction to Magma. The University of Sydney, Sydney (1994)
Galindo, C., Hernando, F., Ruano, D.: New quantum codes from evaluation and matrix-product codes. Finite Fields Their Appl. 36, 98–120 (2015)
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)
Jin, L., Xing, C.: A construction of new quantum MDS codes. IEEE Trans. Inf. Theory 60(5), 2921–2925 (2014)
La Guardia, G.G.: Quantum Error Correction. Springer, Berlin (2020)
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)
Liu, X.S., Yu, L., Hu, P.: New entanglement-assisted quantum codes from \(k\)-Galois dual codes. Finite Field Appl. 55, 21–32 (2019)
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)
Steane, A.M.: Multiple-particle interference and quantum error correction. Phys. Proc. Math. Phys. Eng. Sci. 452(1954), 2551–2577 (1996)
Sok, L.: New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes. arXiv:2110.00769v1
Verma, R.K., Prakash, O., Singh, A., Islam, H.: New quantum codes from skew constacyclic codes. Adv. Math. Commun. (2021). https://doi.org/10.3934/amc.2021028
Zhang, T., Ge, G.: Quantum codes from generalized Reed–Solomon codes and matrix-product codes. arXiv:1508.00978v1
Acknowledgements
This work was supported by Research Funds of Hubei Province, Grant No. D20144401.
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Zhang, X. Hermitian self-orthogonal matrix product codes and their applications to quantum codes. Quantum Inf Process 23, 108 (2024). https://doi.org/10.1007/s11128-024-04314-z
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DOI: https://doi.org/10.1007/s11128-024-04314-z