Some quantum MDS codes from GRS codes

References

• Bennett CH, DiVincenzo DP, Smolin JA, et al. Mixed-state entanglement and quantum error correction. Phys Rev A. 1996;54(5):3824–3851.
   PubMed Web of Science ®Google Scholar
• Shor PW. Scheme for reducing decoherence in quantum computer memory. Phys Rev A. 1995;52(4):R2493–R2496.
   PubMed Web of Science ®Google Scholar
• Steane AM. Error correcting codes in quantum theory. Phys Rev Lett. 1996;77(5):793–797.
   PubMed Web of Science ®Google Scholar
• Knill E, Laflamme R. Theory of quantum error-correcting codes. Phys Rev A. 1997;55(2):900–911.
   Web of Science ®Google Scholar
• Scott AJ. Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions. Phys Rev A. 2004;69(5):052330.
   Web of Science ®Google Scholar
• Calderbank AR, Rains EM, Shor P, et al. Quantum error correction via codes over GF(4). IEEE Trans Inf Theory. 1998;44(4):1369–1387.
   Web of Science ®Google Scholar
• Ketkar A, Klappenecker A, Kumar S, et al. Nonbinary stabilizer codes over finite fields. IEEE Trans Inf Theory. 2006;52(11):4892–4914.
   Web of Science ®Google Scholar
• Sarvepalli PK, Klappenecker A. Nonbinary quantum reed-muller codes. In: Proceedings of International Symposium on Information Theory (ISIT); 2005 Sep 4–9; Adelaide, SA, Australia. IEEE. p. 1023–1027.
   Google Scholar
• Li Z, Xing L-J, Wang X-M. Quantum generalized Reed–Solomon codes: unified framework for quantum maximum-distance-separable codes. Phys Rev A. 2008;77(1):012308.
   Web of Science ®Google Scholar
• Jin L, Ling S, Luo J, et al. Application of classical Hermitian self-orthogonal MDS codes to quantum MDS codes. IEEE Trans Inf Theory. 2010;56(9):4735–4740.
   Web of Science ®Google Scholar
• Aly SA, Klappenecker A, Sarvepalli PK. On quantum and classical BCH codes. IEEE Trans Inf Theory. 2007;53(3):1183–1188.
   Web of Science ®Google Scholar
• Miao S, Senger C. Dual-containing alternant codes for applications in the Calderbank-Shor-Steane construction. In: 2021 IEEE International Symposium on Information Theory (ISIT); 2021 Jul 12–20; Melbourne, Australia. IEEE. p. 2226–2231.
   Google Scholar
• Postol MS. A proposed quantum low density parity check code. arXiv preprint quant-ph/0108131 (2001).
   Google Scholar
• Rains EM. Nonbinary quantum codes. IEEE Trans Inf Theory. 1999;45(6):1827–1832.
   Web of Science ®Google Scholar
• Rotteler M, Grass M, Beth T. On quantum MDS codes. In: Proceedings of International Symposium on Information Theory (ISIT); 2004 Jun 27–Jul 2; Chicago, IL, USA. IEEE. p. 356–356.
   Google Scholar
• Grassl M, Beth T, Roetteler M. On optimal quantum codes. Int J Quantum Inf. 2004;2(1):55–64.
   Web of Science ®Google Scholar
• Jin L, Xing C. A construction of new quantum MDS codes. IEEE Trans Inf Theory. 2014;60(5):2921–2925.
   Web of Science ®Google Scholar
• La Guardia GG. New quantum MDS codes. IEEE Trans Inf Theory. 2011;57(8):5551–5554.
   Web of Science ®Google Scholar
• Kai X, Zhu S. New quantum MDS codes from negacyclic codes. IEEE Trans Inf Theory. 2012;59(2):1193–1197.
   Web of Science ®Google Scholar
• Kai X, Zhu S, Li P. Constacyclic codes and some new quantum MDS codes. IEEE Trans Inf Theory. 2014;60(4):2080–2086.
   Web of Science ®Google Scholar
• Grassl M, Rötteler M. Quantum MDS codes over small fields. In: 2015 IEEE International Symposium on Information Theory (ISIT); 2015 Jun 14–19; Hong Kong, China. IEEE. p. 1104–1108.
   Google Scholar
• Chen B, Ling S, Zhang G. Application of constacyclic codes to quantum MDS codes. IEEE Trans Inf Theory. 2015;61(3):1474–1484.
   Web of Science ®Google Scholar
• Wang L, Zhu S. New quantum MDS codes derived from constacyclic codes. Quantum Inf Process. 2015;14(3):881–889.
   Web of Science ®Google Scholar
• Li S, Xiong M, Ge G. Pseudo-cyclic codes and the construction of quantum MDS codes. IEEE Trans Inf Theory. 2016;62(4):1703–1710.
   Web of Science ®Google Scholar
• Zhang T, Ge G. Quantum codes derived from certain classes of polynomials. IEEE Trans Inf Theory. 2016;62(11):6638–6643.
   Web of Science ®Google Scholar
• Li R, Xu Z. Construction of n,n−4,3q quantum codes for odd prime power q. Phys Rev A. 2010;82(5):052316.
   Web of Science ®Google Scholar
• Hu D, Tang W, Zhao M, et al. Graphical nonbinary quantum error-correcting codes. Phys Rev A. 2008;78(1):012306.
   Web of Science ®Google Scholar
• Feng K. Quantum codes 6,2,3p and 7,3,3p(p≥3) exist. IEEE Trans Inf Theory. 2006;48(8):2384–2391.
   Google Scholar
• Schlingemann D, Werner RF. Quantum error-correcting codes associated with graphs. Phys Rev A. 2001;65(1):012308.
   Web of Science ®Google Scholar
• Fang W, Fu FW. Some new constructions of quantum MDS codes. IEEE Trans Inf Theory. 2019;65(12):7840–7847.
   Web of Science ®Google Scholar
• Fang W, Fu F-W. Two new classes of quantum MDS codes. Finite Fields Their Appl. 2018;53:85–98.
   Web of Science ®Google Scholar
• Fang X, Luo J. New quantum MDS codes over finite fields. Quantum Inf Process. 2020;19(1):1–17.
   Web of Science ®Google Scholar
• Jin L, Kan H, Wen J. Quantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codes. Des Codes Cryptogr. 2017;84(3):463–471.
   Web of Science ®Google Scholar
• Shi X, Yue Q, Chang Y. Some quantum MDS codes with large minimum distance from generalized Reed–Solomon codes. Cryptogr Commun. 2018;10(6):1165–1182.
   Google Scholar
• Shi X, Yue Q, Zhu X. Construction of some new quantum MDS codes. Finite Fields Their Appl. 2017;46:347–362.
   Web of Science ®Google Scholar
• Zhang T, Ge G. Quantum MDS codes with large minimum distance. Des Codes Cryptogr. 2017;83(3):503–517.
   Web of Science ®Google Scholar
• Guo G, Li R, Liu Y. Application of Hermitian self-orthogonal GRS codes to some quantum MDS codes. Finite Fields Their Appl. 2021;76:101901.
   Web of Science ®Google Scholar