{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:27:23Z","timestamp":1761060443398,"version":"3.37.3"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T00:00:00Z","timestamp":1508716800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s11128-017-1748-y","type":"journal-article","created":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T17:47:55Z","timestamp":1508780875000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Two Gilbert\u2013Varshamov-type existential bounds for asymmetric quantum error-correcting codes"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5085-8879","authenticated-orcid":false,"given":"Ryutaroh","family":"Matsumoto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,23]]},"reference":[{"issue":"7","key":"1748_CR1","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1109\/18.959288","volume":"47","author":"A Ashikhmin","year":"2001","unstructured":"Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Trans. Inform. Theory 47(7), 3065\u20133072 (2001)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"1748_CR2","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRevLett.78.405","volume":"78","author":"AR Calderbank","year":"1997","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)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"1748_CR3","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inform. Theory 44(4), 1369\u20131387 (1998)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"1748_CR4","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1103\/PhysRevA.54.1098","volume":"54","author":"AR Calderbank","year":"1996","unstructured":"Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098\u20131105 (1996)","journal-title":"Phys. Rev. A"},{"issue":"12","key":"1748_CR5","doi-asserted-by":"crossref","first-page":"2585","DOI":"10.1103\/PhysRevLett.77.2585","volume":"77","author":"A Ekert","year":"1996","unstructured":"Ekert, A., Macchiavello, C.: Quantum error correction for communication. Phys. Rev. Lett. 77(12), 2585\u20132588 (1996)","journal-title":"Phys. Rev. Lett."},{"issue":"12","key":"1748_CR6","doi-asserted-by":"publisher","first-page":"3323","DOI":"10.1109\/TIT.2004.838088","volume":"50","author":"K Feng","year":"2004","unstructured":"Feng, K., Ma, Z.: A finite Gilbert\u2013Varshamov bound for pure stabilizer quantum codes. IEEE Trans. Inform. Theory 50(12), 3323\u20133325 (2004). doi:\n                        10.1109\/TIT.2004.838088","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1748_CR7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2755682","author":"C Galindo","year":"2017","unstructured":"Galindo, C., Geil, O., Hernando, F., Ruano, D.: Improved constructions of nested code pairs. IEEE Trans. Inform. Theory (2017). doi:\n                        10.1109\/TIT.2017.2755682","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"1748_CR8","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1103\/PhysRevA.54.1862","volume":"54","author":"D Gottesman","year":"1996","unstructured":"Gottesman, D.: Class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A 54(3), 1862\u20131868 (1996)","journal-title":"Phys. Rev. A"},{"key":"1748_CR9","doi-asserted-by":"publisher","first-page":"032345","DOI":"10.1103\/PhysRevA.75.032345","volume":"75","author":"L Ioffe","year":"2007","unstructured":"Ioffe, L., M\u00e9zard, M.: Asymmetric quantum error-correcting codes. Phys. Rev. A 75, 032345 (2007). doi:\n                        10.1103\/PhysRevA.75.032345","journal-title":"Phys. Rev. A"},{"key":"1748_CR10","doi-asserted-by":"publisher","unstructured":"Jin, L., Xing, C.: Quantum Gilbert\u2013Varshamov bound through symplectic self-orthogonal codes. In: Proceedings 2011 IEEE International Symposium on Information Theory, pp. 455\u2013458. Sait Petersburg, Russia (2011). doi:\n                        10.1109\/ISIT.2011.6034167","DOI":"10.1109\/ISIT.2011.6034167"},{"key":"1748_CR11","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. Elsevier, Amsterdam (1977)"},{"issue":"9","key":"1748_CR12","doi-asserted-by":"publisher","first-page":"4391","DOI":"10.1063\/1.1497999","volume":"43","author":"R Matsumoto","year":"2002","unstructured":"Matsumoto, R., Uyematsu, T.: Lower bound for the quantum capacity of a discrete memoryless quantum channel. Jo. Math. Phys. 43(9), 4391\u20134403 (2002). doi:\n                        10.1063\/1.1497999","journal-title":"Jo. Math. Phys."},{"key":"1748_CR13","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"issue":"2105","key":"1748_CR14","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1098\/rspa.2008.0439","volume":"465","author":"PK Sarvepalli","year":"2009","unstructured":"Sarvepalli, P.K., Klappenecker, A., R\u00f6tteler, M.: Asymmetric quantum codes: constructions, bounds and performance. Proc. R. Soc. A Math. Phys. Eng. Sci. 465(2105), 1645\u20131672 (2009). doi:\n                        10.1098\/rspa.2008.0439","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"issue":"1954","key":"1748_CR15","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1098\/rspa.1996.0136","volume":"452","author":"AM Steane","year":"1996","unstructured":"Steane, A.M.: Multiple particle interference and quantum error correction. Proc. R. Soc. Lond. Ser. A 452(1954), 2551\u20132577 (1996)","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"issue":"6","key":"1748_CR16","doi-asserted-by":"publisher","first-page":"4741","DOI":"10.1103\/PhysRevA.54.4741","volume":"54","author":"AM Steane","year":"1996","unstructured":"Steane, A.M.: Simple quantum error-correcting codes. Phys. Rev. A 54(6), 4741\u20134751 (1996). doi:\n                        10.1103\/PhysRevA.54.4741","journal-title":"Phys. Rev. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-017-1748-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-017-1748-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-017-1748-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,11,23]],"date-time":"2017-11-23T10:14:47Z","timestamp":1511432087000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-017-1748-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,23]]},"references-count":16,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["1748"],"URL":"https:\/\/doi.org\/10.1007\/s11128-017-1748-y","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2017,10,23]]},"article-number":"285"}}