{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T20:45:53Z","timestamp":1785530753123,"version":"3.56.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Foundation for Professor and Doctoral of Huizhou University","award":["2016JB005"],"award-info":[{"award-number":["2016JB005"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s10623-017-0413-x","type":"journal-article","created":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T04:02:14Z","timestamp":1505448134000},"page":"1565-1572","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":74,"title":["On MDS linear complementary dual codes and entanglement-assisted quantum codes"],"prefix":"10.1007","volume":"86","author":[{"given":"Jianfa","family":"Qian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lina","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,9,15]]},"reference":[{"key":"413_CR1","doi-asserted-by":"crossref","first-page":"052313","DOI":"10.1103\/PhysRevA.66.052313","volume":"66","author":"G Bowen","year":"2002","unstructured":"Bowen G.: Entanglement required in achieving entanglement-assisted channel capacities. Phys. Rev. A 66, 052313 (2002).","journal-title":"Phys. Rev. A"},{"key":"413_CR2","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1126\/science.1131563","volume":"314","author":"TA Brun","year":"2006","unstructured":"Brun T.A., Devetak I., Hsieh M.H.: Correcting quantum errors with entanglement. Science 314, 436\u2013439 (2006).","journal-title":"Science"},{"key":"413_CR3","doi-asserted-by":"crossref","unstructured":"Carlet C. and Guilley S.: Complementary dual codes for counter-measures to side- channel attacks. In: Coding Theory and Applications, pp.97-105 (2015).","DOI":"10.1007\/978-3-319-17296-5_9"},{"key":"413_CR4","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/TIT.2015.2388576","volume":"61","author":"B Chen","year":"2015","unstructured":"Chen B., Ling S., Zhang G.: Application of constacyclic codes to quantum MDS codes. IEEE Trans. Inf. Theory 61, 1474\u20131484 (2015).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"413_CR5","unstructured":"Ding C., Li C., and Li S.: LCD cyclic codes over finite fields, arxiv: 1608.02170 (2016)."},{"issue":"02","key":"413_CR6","doi-asserted-by":"crossref","first-page":"1350020","DOI":"10.1142\/S1793557113500204","volume":"6","author":"HQ Dinh","year":"2013","unstructured":"Dinh H.Q.: On repeated-root constacyclic codes of length $$4p^s$$ 4 p s . Asian-European J. Math. 6(02), 1350020 (2013).","journal-title":"Asian-European J. Math."},{"key":"413_CR7","unstructured":"Dougherty S. T., Kim J. L., Ozkaya B., Sok L. and Sole P.: The combinatorics of LCD codes: linear programming bound and orthogonal matrices, arxiv: 1506.01955 (2015)."},{"key":"413_CR8","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ffa.2009.01.002","volume":"15","author":"M Esmaeili","year":"2009","unstructured":"Esmaeili M., Yari S.: On complementary-dual quasi-cyclic codes. Finite Fields Appl. 15, 375\u2013386 (2009).","journal-title":"Finite Fields Appl."},{"key":"413_CR9","first-page":"423","volume":"16","author":"J Fan","year":"2016","unstructured":"Fan J., Chen H., Xu J.: Construction of $$q$$ q -ary entanglement-assisted quantum MDS codes with minimum distance greater than $$q + 1$$ q + 1 . Quantum Inf. Comput. 16, 423\u2013434 (2016).","journal-title":"Quantum Inf. Comput."},{"key":"413_CR10","doi-asserted-by":"crossref","first-page":"042338","DOI":"10.1103\/PhysRevA.82.042338","volume":"82","author":"Y Fujiwara","year":"2010","unstructured":"Fujiwara Y., Clark D., Vandendriessche P., Boeck M.D., Tonchev V.D.: Entanglement-assisted quantum low-density parity-check codes. Phys. Rev. A 82, 042338 (2010).","journal-title":"Phys. Rev. A"},{"key":"413_CR11","doi-asserted-by":"publisher","unstructured":"Guenda K., Jitman S., Gulliver T.A.: Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. doi: 10.1007\/s10623-017-0330-z (2016).","DOI":"10.1007\/s10623-017-0330-z"},{"key":"413_CR12","doi-asserted-by":"crossref","first-page":"1550002","DOI":"10.1142\/S0219749915500021","volume":"13","author":"L Guo","year":"2015","unstructured":"Guo L., Fu Q., Li R., Lu L.: Maximal entanglement entanglement-assisted quantum codes of distance three. Int. J. Quantum Inf. 13, 1550002 (2015).","journal-title":"Int. J. Quantum Inf."},{"key":"413_CR13","doi-asserted-by":"crossref","first-page":"062313","DOI":"10.1103\/PhysRevA.76.062313","volume":"76","author":"MH Hsieh","year":"2007","unstructured":"Hsieh M.H., Devetak I., Brun T.A.: General entanglement-assisted quantum error-correcting codes. Phys. Rev. A 76, 062313 (2007).","journal-title":"Phys. Rev. A"},{"key":"413_CR14","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1109\/TIT.2011.2104590","volume":"57","author":"MH Hsieh","year":"2011","unstructured":"Hsieh M.H., Yen W.T., Hsu L.Y.: High performance entanglement-assisted quantum LDPC codes need little entanglement. IEEE Trans. Inf. Theory 57, 1761\u20131769 (2011).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"413_CR15","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511807077","volume-title":"Fundamentals of Error-Correcting Codes","author":"WC Huffman","year":"2003","unstructured":"Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)."},{"key":"413_CR16","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TIT.2014.2308180","volume":"60","author":"X Kai","year":"2014","unstructured":"Kai X., Zhu S., Li P.: Constacyclic codes and some new quantum MDS codes. IEEE Trans. Inf. Theory 60, 2080\u20132086 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"413_CR17","doi-asserted-by":"publisher","unstructured":"Lai C.Y., Ashikhmin A.: Linear programming bounds for entanglement-assisted quantum error-correcting codes by split weight enumerators. IEEE Trans. Inf. Theory. doi: 10.1109\/TIT.2017.2711601 (2017).","DOI":"10.1109\/TIT.2017.2711601"},{"key":"413_CR18","doi-asserted-by":"crossref","first-page":"4020","DOI":"10.1109\/TIT.2013.2246274","volume":"59","author":"CY Lai","year":"2013","unstructured":"Lai C.Y., Brun T.A., Wilde M.M.: Duality in entanglement-assisted quantum error correction. IEEE Trans. Inf. Theory 59, 4020\u20134024 (2013).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"413_CR19","doi-asserted-by":"crossref","first-page":"4427","DOI":"10.1007\/s11128-015-1143-5","volume":"14","author":"R Li","year":"2015","unstructured":"Li R., Li X., Guo L.: On entanglement-assisted quantum codes achieving the entanglement-assisted Griesmer bound. Quantum Inform. Process. 14, 4427\u20134447 (2015).","journal-title":"Quantum Inform. Process."},{"key":"413_CR20","unstructured":"Li S., Ding C., and Liu H.: Parameters of two classes of LCD BCH codes. arxiv: 1608.02670 (2016)."},{"key":"413_CR21","unstructured":"Liu X., Liu H.: Matrix-product complementary dual codes. arxiv: 1604.03774 (2016)."},{"key":"413_CR22","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s11128-014-0830-y","volume":"14","author":"L Lu","year":"2015","unstructured":"Lu L., Li R., Guo L., Fu Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quantum Inform. Process. 14, 165\u2013182 (2015).","journal-title":"Quantum Inform. Process."},{"key":"413_CR23","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 (1977)."},{"issue":"107","key":"413_CR24","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0012-365X(92)90563-U","volume":"106","author":"JL Massey","year":"1992","unstructured":"Massey J.L.: Linear codes with complementary duals. Discret. Math. 106(107), 337\u2013342 (1992).","journal-title":"Discret. Math."},{"key":"413_CR25","unstructured":"Mesnager S., Tang C., Qi Y.: Complementary dual algebraic geometry codes. arXiv:1609.05649 (2016)."},{"key":"413_CR26","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10623-014-9997-6","volume":"77","author":"J Qian","year":"2015","unstructured":"Qian J., Zhang L.: Entanglement-assisted quantum codes from arbitrary binary linear codes. Des. Codes Cryptogr. 77, 193\u2013202 (2015).","journal-title":"Des. Codes Cryptogr."},{"key":"413_CR27","doi-asserted-by":"crossref","unstructured":"Qian J., Zhang L.: Two class of entanglement-assisted quantum codes from shortened Hamming codes. In: 2016 International Conference on Signal and Image Processing, pp. 347\u2013351 (2016).","DOI":"10.1109\/SIPROCESS.2016.7888282"},{"key":"413_CR28","unstructured":"Sari M., Koroglu M. E.: On MDS negacyclic LCD codes. arxiv: 1611.06371 (2016)."},{"key":"413_CR29","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.disc.2004.05.005","volume":"285","author":"N Sendrier","year":"2004","unstructured":"Sendrier N.: Linear codes with complementary duals meet the Gilbert\u2013Varshamov bound. Discret. Math. 285, 345\u2013347 (2004).","journal-title":"Discret. Math."},{"key":"413_CR30","doi-asserted-by":"crossref","first-page":"064302","DOI":"10.1103\/PhysRevA.77.064302","volume":"77","author":"MM Wilde","year":"2008","unstructured":"Wilde M.M., Brun T.A.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A 77, 064302 (2008).","journal-title":"Phys. Rev. A"},{"key":"413_CR31","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/0012-365X(94)90283-6","volume":"126","author":"X Yang","year":"1994","unstructured":"Yang X., Massey J.L.: The necessary and sufficient condition for a cyclic code to have a complementary dual. Discret. Math. 126, 391\u2013393 (1994).","journal-title":"Discret. Math."},{"key":"413_CR32","unstructured":"Zhu S., Pang B. and Sun Z.: The reversible negacyclic codes over finite fields. arXiv: 1610.08206 (2016)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-017-0413-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-017-0413-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-017-0413-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T14:13:33Z","timestamp":1570112013000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-017-0413-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,15]]},"references-count":32,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["413"],"URL":"https:\/\/doi.org\/10.1007\/s10623-017-0413-x","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,15]]}}}