Liu, Xiusheng; Yu, Long; Liu, Hualu New quantum codes from Hermitian dual-containing codes. (English) Zbl 1412.81114 Int. J. Quantum Inf. 17, No. 1, Article ID 1950006, 11 p. (2019). Summary: Hermitian dual-containing codes play an important role in the constructing quantum codes. In this paper, we present a new criterion of Hermitian dual-containing code based on the rank of generator matrix for a linear code. Then, using the criterion, we construct a class of new quantum maximum-distance-separable (MDS) codes and some new quantum codes. Cited in 3 Documents MSC: 81P70 Quantum coding (general) Keywords:Hermitian dual-containing; quantum MDS code; rank of generator matrix PDFBibTeX XMLCite \textit{X. Liu} et al., Int. J. Quantum Inf. 17, No. 1, Article ID 1950006, 11 p. (2019; Zbl 1412.81114) Full Text: DOI References: [1] Calderbank, A. R., Rains, E. M., Shor, P. W. and Sloane, N. J. A., IEEE Trans. Inf. Theory44 (1998) 1369. [2] Kai, X., Zhu, S. and Li, P., IEEE Trans. Inf. Theory60(4) (2014) 2080. [3] Chen, B., Ling, S. and Zhang, G., IEEE Trans. Inform. Theory61(3) (2015) 1474. [4] Li, S., Xiong, M. and Ge, G., IEEE Trans. Inform. Theory64(4) (2016) 1703. [5] Liu, X. S. and Liu, H., Quantum Inf. Process16 (2017) 240. https://doi.org/10.1007/s11128-017-1695-7 [6] Huffman, W. C. and Pless, V., Fundamentals of Error-Correcting Codes (Cambridge University Press, Cambridge, 2003). · Zbl 1099.94030 [7] X. S. Liu, H. Q. Dinh, H. Liu and L. Yu, Cryptogr. Commun., doi: 10.1007/s12095-017-0242-9. [8] Shor, P. W., Phys. Rev. A.52(4) (1995) 2493. [9] Steane, A. M., Phys. Rev. A.54 (1996) 4741. [10] La Guardia, G. G., IEEE Trans. Inf. Theory57(8) (2011) 5551. [11] Kai, X. and Zhu, S., IEEE Trans. Inf. Theory59(2) (2013) 1193. [12] Aly, S. A., Klappenecker, A. and Sarvepalli, P. K., IEEE Trans. Inf. Theory53 (2007) 1183. [13] Ashikhmin, A. and Knill, E., IEEE Trans. Inf. Theory47 (2001) 3065. [14] Y. Edel, Some good quantum twisted codes, online available at https://www.mathi.uni-heidelberg.de/∼yves/Matritzen/QTBCH/QTBCHIndex.html. · Zbl 0963.94049 [15] Ling, S. and Xing, C. P., Coding Theory — A First Course (Cambridge University Press, Cambridge, 2004). [16] Jin, L. and Xing, C., IEEE Trans. Inf. Theory63(3) (2017) 1434. [17] Horn, P. R. and Johnson, C. R., Matrix Analysis (Cambridge University Press, Cambridge, 1985). · Zbl 0576.15001 [18] Zhang, T. and Ge, G., IEEE Trans. Inform. Theory61(3) (2015) 1474. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.