{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T07:35:15Z","timestamp":1781768115789,"version":"3.54.5"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62092003"],"award-info":[{"award-number":["62092003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-022-03742-z","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T10:05:03Z","timestamp":1669370703000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["New constructions of quantum MDS codes over finite fields"],"prefix":"10.1007","volume":"21","author":[{"given":"Renjie","family":"Jin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinquan","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolei","family":"Fang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Longjiang","family":"Qu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"issue":"7","key":"3742_CR1","doi-asserted-by":"publisher","first-page":"3065","DOI":"10.1109\/18.959288","volume":"47","author":"A Ashikhmin","year":"2001","unstructured":"Ashikhmin, A., Knill, E.: Nonbinary quantum stablizer codes. IEEE Trans. Inf. Theory 47(7), 3065\u20133072 (2001)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"3742_CR2","doi-asserted-by":"publisher","first-page":"3796","DOI":"10.1109\/TIT.2022.3150277","volume":"68","author":"S Ball","year":"2022","unstructured":"Ball, S., Vilar, R.: Determining When a Truncated Generalised Reed-Solomon Code Is Hermitian Self-Orthogonal. IEEE Trans. Inf. Theory 68(6), 3796\u20133805 (2022)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"3742_CR3","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/18.746771","volume":"45","author":"M Blaum","year":"1999","unstructured":"Blaum, M., Roth, R.M.: On lowest density MDS codes. IEEE Trans. Inf. Theory 45(1), 46\u201359 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3742_CR4","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1126\/science.1131563","volume":"314","author":"T Brun","year":"2006","unstructured":"Brun, T., Devetak, I., Hsieh, M.H.: Correcting quantum errors with entanglement. Science 314, 436\u2013439 (2006)","journal-title":"Science"},{"issue":"4","key":"3742_CR5","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.M., et al.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44(4), 1369\u20131387 (1998)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3742_CR6","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.ffa.2018.06.003","volume":"53","author":"W Fang","year":"2018","unstructured":"Fang, W., Fu, F.: Two new classes of quantum MDS codes. Finite Fields and Their Appl. 53, 85\u201398 (2018)","journal-title":"Finite Fields and Their Appl."},{"issue":"12","key":"3742_CR7","doi-asserted-by":"publisher","first-page":"7840","DOI":"10.1109\/TIT.2019.2939114","volume":"65","author":"W Fang","year":"2019","unstructured":"Fang, W., Fu, F.: Some new constructions of quantum MDS codes. IEEE Trans. Inf. Theory 65(12), 7840\u20137847 (2019)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"3742_CR8","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/s11128-019-2506-0","volume":"19","author":"X Fang","year":"2020","unstructured":"Fang, X., Luo, J.: New quantum MDS codes over Finite Fields. Quantum Inf. Process. 19(1), 16 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"3742_CR9","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1142\/S0219749904000079","volume":"2","author":"M Grassl","year":"2004","unstructured":"Grassl, M., Beth, T., Rottler, M.: On optimal quantum codes. Int. J. Quantum Inf. 2(1), 757\u2013775 (2004)","journal-title":"Int. J. Quantum Inf."},{"key":"3742_CR10","doi-asserted-by":"crossref","unstructured":"Grassl, M., Rottler, M.: Quantum MDS codes over small fields. In Proceedings of the International Symposium on Information Theory (ISIT), pp. 1104\u20131108 (2015)","DOI":"10.1109\/ISIT.2015.7282626"},{"issue":"8","key":"3742_CR11","doi-asserted-by":"publisher","first-page":"5551","DOI":"10.1109\/TIT.2011.2159039","volume":"57","author":"GLG Guardia","year":"2011","unstructured":"Guardia, G.L.G.: New quantum MDS codes. IEEE Trans. Inf. Theory 57(8), 5551\u20135554 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"3742_CR12","doi-asserted-by":"publisher","first-page":"2745","DOI":"10.1007\/s11128-016-1311-2","volume":"15","author":"X He","year":"2016","unstructured":"He, X., Xu, L., Chen, H.: New $$q$$-ary quantum MDS codes with distances bigger than $$\\frac{q}{2}$$. Quantum Inf. Process. 15(7), 2745\u20132758 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"3742_CR13","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10623-016-0281-9","volume":"84","author":"L Jin","year":"2017","unstructured":"Jin, L., Kan, H., Wen, J.: Quantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codes. Des. Codes Cryptogr. 84(3), 463\u2013471 (2017)","journal-title":"Des. Codes Cryptogr."},{"issue":"9","key":"3742_CR14","doi-asserted-by":"publisher","first-page":"4735","DOI":"10.1109\/TIT.2010.2054174","volume":"56","author":"L Jin","year":"2010","unstructured":"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\u20134740 (2010)","journal-title":"IEEE. Trans. Inf. Theory"},{"issue":"5","key":"3742_CR15","doi-asserted-by":"publisher","first-page":"2921","DOI":"10.1109\/TIT.2014.2299800","volume":"60","author":"L Jin","year":"2014","unstructured":"Jin, L., Xing, C.: A construction of new quantum MDS codes. IEEE Trans. Inf. Theory 60(5), 2921\u20132925 (2014)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"3742_CR16","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1109\/TIT.2012.2220519","volume":"59","author":"X Kai","year":"2012","unstructured":"Kai, X., Zhu, S.: New quantum MDS codes from negacyclic codes. IEEE Trans. Inf. Theory 59(2), 1193\u20131197 (2012)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"3742_CR17","doi-asserted-by":"publisher","first-page":"4892","DOI":"10.1109\/TIT.2006.883612","volume":"52","author":"A Ketkar","year":"2006","unstructured":"Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52(11), 4892\u20134914 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"3742_CR18","doi-asserted-by":"publisher","first-page":"012308-1","DOI":"10.1103\/PhysRevA.77.012308","volume":"77","author":"Z Li","year":"2008","unstructured":"Li, Z., Xing, L., Wang, X.: Quantum generalized Reed\u2013Solomon codes: unified framework for quantum MDS codes. Phys. Rev. A 77(1), 012308-1\u2013012308-4 (2008)","journal-title":"Phys. Rev. A"},{"key":"3742_CR19","volume-title":"The Theory of Error-Correcting Codes","author":"FJ MacWilliams","year":"1977","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North Holland, Amsterdam, The Netherlands (1977)"},{"issue":"6","key":"3742_CR20","doi-asserted-by":"publisher","first-page":"1827","DOI":"10.1109\/18.782103","volume":"45","author":"EM Rains","year":"1999","unstructured":"Rains, E.M.: Nonbinary quantum codes. IEEE Trans. Inf. Theory 45(6), 1827\u20131832 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3742_CR21","doi-asserted-by":"crossref","unstructured":"R\u00f3ttler, M., Grassl, M., Beth, T.: On quantum MDS codes. In Proceedings of the International Symposium on Information Theory, Chicago, USA, 356 (2004)","DOI":"10.1109\/ISIT.2004.1365393"},{"issue":"6","key":"3742_CR22","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1007\/s12095-017-0274-1","volume":"10","author":"X Shi","year":"2017","unstructured":"Shi, X., Yue, Q., Chang, Y.: Some quantum MDS codes with large minimum distance from generalized Reed-Solomon codes. Cryptogr. Commun. 10(6), 1165\u20131182 (2017)","journal-title":"Cryptogr. Commun."},{"key":"3742_CR23","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.ffa.2017.04.002","volume":"46","author":"X Shi","year":"2017","unstructured":"Shi, X., Yue, Q., Zhu, X.: Construction of some new quantum MDS codes. Finite Fields Their Appl. 46, 347\u2013362 (2017)","journal-title":"Finite Fields Their Appl."},{"issue":"7","key":"3742_CR24","doi-asserted-by":"publisher","first-page":"1989","DOI":"10.1016\/j.disc.2019.03.019","volume":"342","author":"X Shi","year":"2019","unstructured":"Shi, X., Yue, Q., Wu, Y.: New quantum MDS codes with large minimum distance and short length from generalized Reed-Solomon codes. Discrete Math. 342(7), 1989\u20132001 (2019)","journal-title":"Discrete Math."},{"issue":"3","key":"3742_CR25","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s10623-016-0245-0","volume":"83","author":"T Zhang","year":"2017","unstructured":"Zhang, T., Ge, G.: Quantum MDS codes with large minimum distance. Des. Codes Cryptogr. 83(3), 503\u2013517 (2017)","journal-title":"Des. Codes Cryptogr."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03742-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03742-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03742-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T14:57:11Z","timestamp":1728485831000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03742-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,24]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["3742"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03742-z","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,24]]},"assertion":[{"value":"30 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"395"}}