{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T19:25:09Z","timestamp":1769282709040,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T00:00:00Z","timestamp":1467676800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant Nos. 11431003 and 61571310"],"award-info":[{"award-number":["Grant Nos. 11431003 and 61571310"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s10623-016-0245-0","type":"journal-article","created":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T06:18:11Z","timestamp":1467699491000},"page":"503-517","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["Quantum MDS codes with large minimum distance"],"prefix":"10.1007","volume":"83","author":[{"given":"Tao","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Gennian","family":"Ge","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,5]]},"reference":[{"key":"245_CR1","doi-asserted-by":"crossref","unstructured":"Aly S.A., Klappenecker A., Sarvepalli P.K.: On quantum and classical BCH codes. IEEE Trans. Inform. Theory 53(3), 1183\u20131188 (2007).","DOI":"10.1109\/TIT.2006.890730"},{"key":"245_CR2","doi-asserted-by":"crossref","unstructured":"Ashikhmin A., Knill E.: Nonbinary quantum stabilizer codes. IEEE Trans. Inform. Theory 47(7), 3065\u20133072 (2001).","DOI":"10.1109\/18.959288"},{"key":"245_CR3","doi-asserted-by":"crossref","unstructured":"Bierbrauer J., Edel Y.: Quantum twisted codes. J. Combin. Des. 8(3), 174\u2013188 (2000).","DOI":"10.1002\/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T"},{"key":"245_CR4","doi-asserted-by":"crossref","unstructured":"Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 78(3), 405\u2013408 (1997).","DOI":"10.1103\/PhysRevLett.78.405"},{"key":"245_CR5","doi-asserted-by":"crossref","unstructured":"Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction via codes over $${\\rm GF}(4)$$ GF ( 4 ) . IEEE Trans. Inform. Theory 44(4), 1369\u20131387 (1998).","DOI":"10.1109\/18.681315"},{"key":"245_CR6","doi-asserted-by":"crossref","unstructured":"Chen H., Ling S., Xing C.: Quantum codes from concatenated algebraic\u2013geometric codes. IEEE Trans. Inform. Theory 51(8), 2915\u20132920 (2005).","DOI":"10.1109\/TIT.2005.851760"},{"key":"245_CR7","doi-asserted-by":"crossref","unstructured":"Chen B., Ling S., Zhang G.: Application of constacyclic codes to quantum MDS codes. IEEE Trans. Inform. Theory 61(3), 1474\u20131484 (2015).","DOI":"10.1109\/TIT.2015.2388576"},{"key":"245_CR8","unstructured":"Feng K.: Quantum codes $$[[6,2,3]]_p$$ [ [ 6 , 2 , 3 ] ] p and $$[[7,3,3]]_p (p\\ge 3)$$ [ [ 7 , 3 , 3 ] ] p ( p \u2265 3 ) exist. IEEE Trans. Inform. Theory 48(8), 2384\u20132391 (2002)."},{"key":"245_CR9","doi-asserted-by":"crossref","unstructured":"Grassl M., Rotteler M.: Quantum MDS codes over small fields. In: Proceedings of the International Symposium on Information Theory, pp. 1104\u20131108 (2015).","DOI":"10.1109\/ISIT.2015.7282626"},{"key":"245_CR10","doi-asserted-by":"crossref","unstructured":"Grassl M., Beth T., Roetteler M.: On optimal quantum codes. Int. J. Quantum Inf. 2(01), 55\u201364 (2004).","DOI":"10.1142\/S0219749904000079"},{"key":"245_CR11","doi-asserted-by":"crossref","unstructured":"Jin L., Xing C.: A construction of new quantum MDS codes. IEEE Trans. Inform. Theory 60(5), 2921\u20132925 (2014).","DOI":"10.1109\/TIT.2014.2299800"},{"key":"245_CR12","doi-asserted-by":"crossref","unstructured":"Jin L., Ling S., Luo J., Xing C.: Application of classical Hermitian self-orthogonal MDS codes to quantum MDS codes. IEEE Trans. Inform. Theory 56(9), 4735\u20134740 (2010).","DOI":"10.1109\/TIT.2010.2054174"},{"key":"245_CR13","doi-asserted-by":"crossref","unstructured":"Kai X., Zhu S.: New quantum MDS codes from negacyclic codes. IEEE Trans. Inform. Theory 59(2), 1193\u20131197 (2013).","DOI":"10.1109\/TIT.2012.2220519"},{"key":"245_CR14","doi-asserted-by":"crossref","unstructured":"Kai X., Zhu S., Li P.: Constacyclic codes and some new quantum MDS codes. IEEE Trans. Inform. Theory 60(4), 2080\u20132086 (2014).","DOI":"10.1109\/TIT.2014.2308180"},{"key":"245_CR15","doi-asserted-by":"crossref","unstructured":"Ketkar A., Klappenecker A., Kumar S., Sarvepalli P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inform. Theory 52(11), 4892\u20134914 (2006).","DOI":"10.1109\/TIT.2006.883612"},{"key":"245_CR16","doi-asserted-by":"crossref","unstructured":"Knill E., Laflamme R.: Theory of quantum error-correcting codes. Phys. Rev. A (3) 55(2), 900\u2013911 (1997).","DOI":"10.1103\/PhysRevA.55.900"},{"key":"245_CR17","doi-asserted-by":"crossref","unstructured":"La Guardia G.G.: New quantum MDS codes. IEEE Trans. Inform. Theory 57(8), 5551\u20135554 (2011).","DOI":"10.1109\/TIT.2011.2159039"},{"key":"245_CR18","doi-asserted-by":"crossref","unstructured":"Laflamme R., Miquel C., Paz J.P., Zurek W.H.: Perfect quantum error correcting code. Phys. Rev. Lett. 77(1), 198 (1996).","DOI":"10.1103\/PhysRevLett.77.198"},{"key":"245_CR19","doi-asserted-by":"crossref","unstructured":"Li Z., Xing L., Wang X.: Quantum generalized Reed\u2013Solomon codes: unified framework for quantum maximum-distance-separable codes. Phys. Rev. A, 77(1), 012308 (2008).","DOI":"10.1103\/PhysRevA.77.012308"},{"key":"245_CR20","doi-asserted-by":"crossref","unstructured":"Rains E.M.: Nonbinary quantum codes. IEEE Trans. Inform. Theory 45(6), 1827\u20131832 (1999).","DOI":"10.1109\/18.782103"},{"key":"245_CR21","doi-asserted-by":"crossref","unstructured":"Steane A.M.: Enlargement of Calderbank\u2013Shor\u2013Steane quantum codes. IEEE Trans. Inform. Theory 45(7), 2492\u20132495 (1999).","DOI":"10.1109\/18.796388"},{"key":"245_CR22","doi-asserted-by":"crossref","unstructured":"Wang L., Zhu S.: New quantum MDS codes derived from constacyclic codes. Quantum Inf. Process. 14(3), 881\u2013889 (2015).","DOI":"10.1007\/s11128-014-0903-y"},{"key":"245_CR23","doi-asserted-by":"crossref","unstructured":"Zhang G., Chen B.: New quantum MDS codes. Int. J. Quantum Inf. 12(4), 1450019 (2014).","DOI":"10.1142\/S0219749914500191"},{"key":"245_CR24","doi-asserted-by":"crossref","unstructured":"Zhang T., Ge G.: Some new classes of quantum MDS codes from constacyclic codes. IEEE Trans. Inform. Theory 61(9), 5224\u20135228 (2015).","DOI":"10.1109\/TIT.2015.2450235"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0245-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-016-0245-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0245-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0245-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T13:50:28Z","timestamp":1498312228000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-016-0245-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,5]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["245"],"URL":"https:\/\/doi.org\/10.1007\/s10623-016-0245-0","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,5]]}}}