{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T11:45:13Z","timestamp":1780919113701,"version":"3.54.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Shandong Provincial Natural Science Foundation, China","award":["ZR2022MA061"],"award-info":[{"award-number":["ZR2022MA061"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61902429"],"award-info":[{"award-number":["61902429"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Graduate Innovation Project of China University of Petroleum","award":["YCX2021137"],"award-info":[{"award-number":["YCX2021137"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-022-03794-1","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T11:14:46Z","timestamp":1674126886000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Non-binary quantum synchronizable codes based on cyclic codes over $$\\textrm{F}_q$$"],"prefix":"10.1007","volume":"22","author":[{"given":"Shiwen","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tongjiang","family":"Yan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuhua","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xueting","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,1,19]]},"reference":[{"issue":"4","key":"3794_CR1","doi-asserted-by":"publisher","first-page":"R2493","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), R2493\u2013R2496 (1995)","journal-title":"Phys. Rev. A"},{"key":"3794_CR2","doi-asserted-by":"publisher","first-page":"2551","DOI":"10.1098\/rspa.1996.0136","volume":"452","author":"A Steane","year":"1996","unstructured":"Steane, A.: Multiple particle interference and quantum error correction. Proc. Math. Phys. Eng. Sci. 452, 2551\u20132557 (1996)","journal-title":"Proc. Math. Phys. Eng. Sci."},{"issue":"2","key":"3794_CR3","doi-asserted-by":"publisher","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\u20131106 (1996)","journal-title":"Phys. Rev. A"},{"key":"3794_CR4","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 Int. Symp. Inf. Theory 44, 1369\u20131387 (1998)","journal-title":"IEEE Int. Symp. Inf. Theory"},{"key":"3794_CR5","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge, New York (2011)","DOI":"10.1017\/CBO9780511976667"},{"key":"3794_CR6","doi-asserted-by":"crossref","unstructured":"Lidar, D.A., Brun, T.A.: Quantum Error Correction. Cambridge, New York (2013)","DOI":"10.1017\/CBO9781139034807"},{"issue":"2","key":"3794_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.022344","volume":"87","author":"Y Fujiwara","year":"2013","unstructured":"Fujiwara, Y.: Block synchronization for quantum information. Phys. Rev. A 87(2), 022344 (2013)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"3794_CR8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.012318","volume":"88","author":"Y Fujiwara","year":"2013","unstructured":"Fujiwara, Y., Tonchev, V.D., Wong, T.W.H.: Algebraic techniques in designing quantum synchronizable codes. Phys. Rev. A 88(1), 012318 (2013)","journal-title":"Phys. Rev. A"},{"issue":"11","key":"3794_CR9","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":"3794_CR10","doi-asserted-by":"crossref","unstructured":"Xie, Y., Yuan, J., Fujiwara, Y.: Quantum synchronizable codes from quadratic residue codes and their supercodes. In: IEEE Information Theory Workshop, pp. 172\u2013176 (2014)","DOI":"10.1109\/ITW.2014.6970815"},{"issue":"3","key":"3794_CR11","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 sychronizable codes. IEEE Commun. Lett. 20(3), 414\u2013417 (2016)","journal-title":"IEEE Commun. Lett."},{"key":"3794_CR12","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s12190-016-1042-7","volume":"55","author":"K Guenda","year":"2016","unstructured":"Guenda, K., La Guardia, G.G., Gulliver, T.A.: Algebraic quantum synchronizable codes. J. Appl. Math. Comput. 55, 393\u2013407 (2016)","journal-title":"J. Appl. Math. Comput."},{"issue":"3","key":"3794_CR13","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 sychronizable codes from repeated-root cyclic codes. IEEE Trans. Inf. Theory 64(3), 1461\u20131470 (2018)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"3794_CR14","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."},{"issue":"9","key":"3794_CR15","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s11128-019-2389-0","volume":"18","author":"L Luo","year":"2019","unstructured":"Luo, L., Ma, Z., Lin, D.: Two new families of quantum synchronizable codes. Quantum Inf. Process. 18(9), 277\u2013294 (2019)","journal-title":"Quantum Inf. Process."},{"key":"3794_CR16","doi-asserted-by":"publisher","first-page":"8449","DOI":"10.1109\/ACCESS.2019.2963289","volume":"8","author":"C Du","year":"2019","unstructured":"Du, C., Ma, Z., Luo, L., et al.: On a family of Quantum synchronizable codes based on the $$\\left(\\lambda (u+v)\\mid u-v\\right)$$ construction. IEEE Access 8, 8449\u20138458 (2019)","journal-title":"IEEE Access"},{"key":"3794_CR17","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s11128-021-03058-4","volume":"20","author":"H Liu","year":"2021","unstructured":"Liu, H., Liu, X.: Quantum synchronizable codes from finite rings. Quantum Inf. Process. 20, 125\u2013144 (2021)","journal-title":"Quantum Inf. Process."},{"key":"3794_CR18","doi-asserted-by":"crossref","unstructured":"Shi, X., Yue, Q., Huang, X.: Quantum synchronizable codes from the Whiteman\u2019s generalized cyclotomy. Cryptogr. Commun. 13 (2021)","DOI":"10.1007\/s12095-021-00501-2"},{"key":"3794_CR19","doi-asserted-by":"crossref","unstructured":"Dinh, H.Q., Nguyen, B.T., Tansuchat, R.: Quantum MDS and synchronizable codes from cyclic codes of length $$5p^s$$ over $${\\rm F}_p^m$$. Appl. Algebra Eng. Commun. Comput. (2021)","DOI":"10.1007\/s00200-021-00531-6"},{"key":"3794_CR20","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1016\/j.ffa.2011.09.005","volume":"18","author":"GK Bakshi","year":"2012","unstructured":"Bakshi, G.K., Raka, M.: A class of constacyclic codes over a finite field. Finite Fields Appl. 18, 362\u2013377 (2012)","journal-title":"Finite Fields Appl."},{"key":"3794_CR21","doi-asserted-by":"crossref","unstructured":"Ling, S., Xing, C.: Coding Theory. Cambridge, New York (2004)","DOI":"10.1017\/CBO9780511755279"},{"key":"3794_CR22","volume-title":"The theory of error-correctiong codes","author":"FJ MacWilliams","year":"1978","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The theory of error-correctiong codes. Elsevier, New York (1978)"},{"key":"3794_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2020.101648","volume":"63","author":"Y Wu","year":"2020","unstructured":"Wu, Y., Yue, Q., Fan, S.: Self-reciprocal and self-conjugate-reciprocal irreducible factors of $$x^n-\\lambda $$ and their applications. Finite Fields their Appl. 63, 101648 (2020)","journal-title":"Finite Fields their Appl."},{"issue":"6","key":"3794_CR24","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1007\/s002000050117","volume":"9","author":"RN Daskalov","year":"1999","unstructured":"Daskalov, R.N., Gulliver, T.A.: Bounds on minimum distance for linear codes over $${\\rm GF}(5)$$. Appl. Algebra Eng. Commun. Comput. 9(6), 547\u2013558 (1999)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"1\u20133","key":"3794_CR25","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/S0012-365X(96)00104-5","volume":"169","author":"IG Boukliev","year":"1997","unstructured":"Boukliev, I.G.: New bounds for the minimum length of quanternary linear codes of dimension five. Discret. Math. 169(1\u20133), 185\u2013192 (1997)","journal-title":"Discret. Math."},{"issue":"6","key":"3794_CR26","doi-asserted-by":"publisher","first-page":"730","DOI":"10.1109\/TIT.1978.1055965","volume":"24","author":"JH VanLint","year":"1978","unstructured":"VanLint, J.H., MacWilliams, F.J.: Generalized quadratic residue codes. IEEE Trans. Inf. Theory 24(6), 730\u2013737 (1978)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3794_CR27","unstructured":"Grassl, M.: Bounds on the minimum distance of linear codes and quantum codes. https:\/\/www.codetables.de (2021)"},{"issue":"3","key":"3794_CR28","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1109\/TIT.2006.890730","volume":"53","author":"SA Aly","year":"2007","unstructured":"Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53(3), 1183\u20131188 (2007)","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03794-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03794-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03794-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T21:59:20Z","timestamp":1676498360000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03794-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,19]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["3794"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03794-1","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,19]]},"assertion":[{"value":"11 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The authors promise that the results of this article are correct and original and it has not been published in other journals before.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors consent to participate.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"All authors consent for publication.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The code generated during this study is included in the supplementary information files.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}],"article-number":"72"}}