{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T15:54:53Z","timestamp":1764431693787},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Research Funds of Hubei Province","award":["D20144401"],"award-info":[{"award-number":["D20144401"]}]},{"name":"Training Program of Innovation and Entrepreneurship for Undergraduates","award":["S202010500054"],"award-info":[{"award-number":["S202010500054"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11128-021-03058-4","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T07:03:01Z","timestamp":1616655781000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantum synchronizable codes from finite rings"],"prefix":"10.1007","volume":"20","author":[{"given":"Hualu","family":"Liu","sequence":"first","affiliation":[]},{"given":"Xiusheng","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"3058_CR1","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1016\/S0019-9958(67)91048-0","volume":"10","author":"RC Bose","year":"1967","unstructured":"Bose, R.C., Caldwell, J.G.: Synchronizable error-correcting codes. Inf. Contr. 10, 616\u2013630 (1967)","journal-title":"Inf. Contr."},{"key":"3058_CR2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The MAGMA algebra system I: the user language. J. Symb. Comput. 24, 235\u2013265 (1997)","journal-title":"J. Symb. Comput."},{"key":"3058_CR3","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.W., Sloane, N.J.A.: Quantum error correction via codes over $$GF(4)$$. IEEE Trans. Inf. Theory 44, 1369\u20131387 (1998)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3058_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ffa.2016.06.007","volume":"42","author":"B Chen","year":"2016","unstructured":"Chen, B., Ling, S., Zhang, G.: Enumeration formulas for self-dual cyclic codes. Finite Fields Appl. 42, 1\u201322 (2016)","journal-title":"Finite Fields Appl."},{"issue":"8","key":"3058_CR5","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1109\/TIT.2004.831789","volume":"50","author":"H Dinh","year":"2004","unstructured":"Dinh, H., L\u00f3pez-Permouth, S.R.: Cyclic and negacyclic codes over finite chain rings. IEEE Trans Inf. Theory 50(8), 1728\u20131744 (2004)","journal-title":"IEEE Trans Inf. Theory"},{"key":"3058_CR6","doi-asserted-by":"publisher","first-page":"124608","DOI":"10.1109\/ACCESS.2020.3006001","volume":"8","author":"H Dinh","year":"2020","unstructured":"Dinh, H., Nguyen, B.T., Yamaka, W.: Quantum MDS and synchronizable codes from cyclic and negacyclic codes of length $$2p^s$$ Over $${\\mathbb{F}}_{p^m}$$. IEEE Access 8, 124608\u2013124623 (2020)","journal-title":"IEEE Access"},{"key":"3058_CR7","doi-asserted-by":"publisher","first-page":"8449","DOI":"10.1109\/ACCESS.2019.2963289","volume":"8","author":"C Du","year":"2020","unstructured":"Du, C., Ma, Z., Luo, L.: On a Family of Quantum Synchronizable Codes Based on the $$(\\lambda (u+v)|u-v)$$ Construction. IEEE Access 8, 8449\u20138458 (2020)","journal-title":"IEEE Access"},{"key":"3058_CR8","doi-asserted-by":"crossref","unstructured":"Fujiwara, Y.: Block synchronization for quantum information. Phys. Rev. A 87(2), 022344 (2013)","DOI":"10.1103\/PhysRevA.87.022344"},{"key":"3058_CR9","doi-asserted-by":"crossref","unstructured":"Fujiwara, Y., Tonchev, V. D., T. Wong, W. H.: Algebraic techniques in designing quantum synchronizable codes. Phy. Rev. A 88(1), 012318 (2013)","DOI":"10.1103\/PhysRevA.88.012318"},{"issue":"11","key":"3058_CR10","doi-asserted-by":"publisher","first-page":"7345","DOI":"10.1109\/TIT.2014.2357029","volume":"60","author":"Y Fujiwara","year":"2014","unstructured":"Fujiwara, Y., Vandendriessche, P.: Quantum synchronizable codes from finite geometries. IEEE Trans. Inf. Theory 60(11), 7345\u20137354 (2014)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3058_CR11","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s12190-016-1042-7","volume":"55","author":"K Guenda","year":"2017","unstructured":"Guenda, K., La Guardia, G.G., Gulliver, T.A.: Algebraic quantum synchronizable codes. J. Appl. Math. Comput. 55, 393\u2013407 (2017)","journal-title":"J. Appl. Math. Comput."},{"key":"3058_CR12","doi-asserted-by":"publisher","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)"},{"issue":"1","key":"3058_CR13","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/LCOMM.2018.2877989","volume":"23","author":"L Li","year":"2019","unstructured":"Li, L., Zhu, S., Liu, L.: Quantum synchronizable codes from the cyclotomy of order four. IEEE Commun. Lett. 23(1), 12\u201315 (2019)","journal-title":"IEEE Commun. Lett."},{"key":"3058_CR14","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1007\/s11128-017-1695-7","volume":"16","author":"X Liu","year":"2017","unstructured":"Liu, X., Liu, H.: Quantum codes from linear codes over finite chain rings. Quantum Inf. Process. 16, 240 (2017)","journal-title":"Quantum Inf. Process."},{"key":"3058_CR15","volume-title":"Finite Fields","author":"R Lidl","year":"1997","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1997)"},{"issue":"3","key":"3058_CR16","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.1109\/TIT.2018.2795479","volume":"64","author":"L Luo","year":"2018","unstructured":"Luo, L., Ma, Z.: Non-binary quantum synchronizable codes from repeated-root cyclic codes. IEEE Trans. Inf. Theory 64(3), 1461\u20131470 (2018)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3058_CR17","doi-asserted-by":"crossref","unstructured":"Luo, L., Ma, Z., Lin, D.: Two new families of quantum synchronizable codes. Quantum Inf. Process. 18, 277 (2019)","DOI":"10.1007\/s11128-019-2389-0"},{"key":"3058_CR18","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/PL00012382","volume":"10","author":"GH Norton","year":"2000","unstructured":"Norton, G.H., S\u01cel\u01cegean, A.: On the structure of linear and cyclic codes over finite chain rings. AAECC 10, 489\u2013506 (2000)","journal-title":"AAECC"},{"issue":"4","key":"3058_CR19","doi-asserted-by":"publisher","first-page":"2493","DOI":"10.1103\/PhysRevA.52.R2493","volume":"52","author":"PW Shor","year":"1995","unstructured":"Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), 2493\u20132496 (1995)","journal-title":"Phys. Rev. A"},{"key":"3058_CR20","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, 4741\u20134751 (1996)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"3058_CR21","first-page":"e14641","volume":"6","author":"Y Xie","year":"2014","unstructured":"Xie, Y., Yuan, J., Fujiwara, Y.: Quantum synchronizable codes from augmentation of cyclic codes. Plos One 6(2), e14641 (2014)","journal-title":"Plos One"},{"issue":"3","key":"3058_CR22","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1109\/LCOMM.2015.2512261","volume":"20","author":"Y Xie","year":"2016","unstructured":"Xie, Y., Yang, L., Yuan, J.: $$q$$-ary chain-containing quantum synchronizable codes. IEEE Commun. Lett. 20(3), 414\u2013417 (2016)","journal-title":"IEEE Commun. Lett."},{"key":"3058_CR23","doi-asserted-by":"publisher","first-page":"2677","DOI":"10.1016\/j.disc.2011.08.015","volume":"311","author":"S Zhu","year":"2011","unstructured":"Zhu, S., Wang, L.: A class of constacyclic codes over $${\\mathbb{F}}_p + v{\\mathbb{F}}_p$$ and its Gray image. Discret. Math. 311, 2677\u20132682 (2011)","journal-title":"Discret. Math."},{"key":"3058_CR24","unstructured":"Zhang, T., Ge, G.: Quantum block and synchronizable codes derived from certain classes of polynomials. arxiv:1508.00974"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03058-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-021-03058-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03058-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T22:57:17Z","timestamp":1617231437000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-021-03058-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["3058"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03058-4","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"13 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"125"}}