{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:06Z","timestamp":1740137226007,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004541","name":"Ministry of Human Resource Development","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004541","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s11128-021-03230-w","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T06:02:48Z","timestamp":1631167368000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New quantum codes from self-orthogonal cyclic codes over $${\\mathbb {F}}_{q^{2}}[u]\/\\langle u^k \\rangle $$"],"prefix":"10.1007","volume":"20","author":[{"given":"Soumak","family":"Biswas","sequence":"first","affiliation":[]},{"given":"Maheshanand","family":"Bhaintwal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"3230_CR1","first-page":"72","volume":"2","author":"MM Al-Ashker","year":"2013","unstructured":"Al-Ashker, M.M., Chen, J.: Cyclic codes of arbitrary length over $$F_q + uF_q + u^2F_q + \\cdots + u^{k-1}F_q$$. Palest. J. Math. 2, 72\u201380 (2013)","journal-title":"Palest. J. Math."},{"key":"3230_CR2","doi-asserted-by":"publisher","first-page":"4089","DOI":"10.1007\/s11128-016-1379-8","volume":"15","author":"M Ashraf","year":"2016","unstructured":"Ashraf, M., Mohammad, G.: Quantum codes from cyclic codes over $$F_q + uF_q + vF_q + uvF_q$$. Quantum Inf. Process 15, 4089\u20134098 (2016)","journal-title":"Quantum Inf. Process"},{"issue":"3","key":"3230_CR3","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1109\/LCOMM.2019.2959529","volume":"24","author":"T Bag","year":"2020","unstructured":"Bag, T., Dinh, H.Q., Upadhyay, A.K., Yamaka, W.: New non-binary quantum codes from cyclic codes over product rings. IEEE Commun. Lett. 24(3), 486\u2013490 (2020)","journal-title":"IEEE Commun. Lett."},{"key":"3230_CR4","volume-title":"Handbook of Magma Functions","author":"W Bosma","year":"1995","unstructured":"Bosma, W., Cannon, J.: Handbook of Magma Functions. Univ. of Sydney, Sydney (1995)"},{"issue":"2","key":"3230_CR5","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\u20131105 (1996)","journal-title":"Phys. Rev. A"},{"key":"3230_CR6","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":"3230_CR7","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":"3230_CR8","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1109\/TIT.2004.831789","volume":"50","author":"HQ Dinh","year":"2004","unstructured":"Dinh, H.Q., Lopez-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"},{"issue":"1","key":"3230_CR9","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.ffa.2009.11.004","volume":"16","author":"ST Dougherty","year":"2010","unstructured":"Dougherty, S.T., Kim, J.L., Kulosman, H., Liu, H.: Self-dual codes over commutative Frobenius rings. Finite Fields Appl. 16(1), 14\u201326 (2010)","journal-title":"Finite Fields Appl."},{"key":"3230_CR10","unstructured":"Edel, Y.: Some good quantum twisted codes. https:\/\/www.mathi.uni-heidelberg.de\/yves\/Matrizen\/QTBCH\/QTBCHIndex.html"},{"issue":"2","key":"3230_CR11","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s00200-018-0366-y","volume":"30","author":"Y Gao","year":"2019","unstructured":"Gao, Y., Gao, J., Fu, F.W.: On Quantum codes from cyclic codes over the ring $${\\mathbb{F}}_q+v_1{\\mathbb{F}}_q+\\cdots +v_r{\\mathbb{F}}_q$$. Appl. Algebra Engg. Comm. Comput. 30(2), 161\u2013174 (2019)","journal-title":"Appl. Algebra Engg. Comm. Comput."},{"key":"3230_CR12","unstructured":"Grassl M.: Bounds on the minimum distance of linear codes and quantum codes, Online available at http:\/\/www.codetables.de Accessed on 2020-07-07"},{"key":"3230_CR13","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1109\/18.312154","volume":"40","author":"AR Hammons","year":"1994","unstructured":"Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Sole, P.: The $$Z_4$$-linearity of Kerdock, Preperata, Goethals and related codes. IEEE Trans. Inf. Theory 40, 301\u2013319 (1994)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"17","key":"3230_CR14","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s11128-020-02825-z","volume":"19","author":"H Islam","year":"2020","unstructured":"Islam, H., Prakash, O.: New quantum codes from constacyclic and additive constacyclic codes. Quantum Inf. Process 19(17), 319 (2020)","journal-title":"Quantum Inf. Process"},{"key":"3230_CR15","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1142\/S0219749911007757","volume":"9","author":"X Kai","year":"2011","unstructured":"Kai, X., Zhu, S.: Quaternary construction of quantum codes from cyclic codes over $${\\mathbb{F}}_4+u{\\mathbb{F}}_4$$. Int. J. Quantum Inf. 9, 689\u2013700 (2011)","journal-title":"Int. J. Quantum Inf."},{"key":"3230_CR16","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10623-011-9500-6","volume":"62","author":"X Kai","year":"2012","unstructured":"Kai, X., Zhu, S.: Negacyclic self-dual codes over finite chain rings. Des. Codes Crypto. 62, 161\u2013174 (2012)","journal-title":"Des. Codes Crypto."},{"key":"3230_CR17","doi-asserted-by":"publisher","first-page":"4892","DOI":"10.1109\/TIT.2006.883612","volume":"52","author":"A Ketkar","year":"2006","unstructured":"Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892\u20134914 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3230_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-016-1481-y","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, 1\u201315 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"3230_CR19","doi-asserted-by":"publisher","first-page":"421","DOI":"10.3934\/amc.2019027","volume":"13","author":"F Ma","year":"2019","unstructured":"Ma, F., Gao, J., Fu, F.W.: New non-binary quantum codes from constacyclic codes over $${\\mathbb{F}}_p[u, v]\/\\langle u^2-1, v^2-v, uv-vu\\rangle $$. Adv. Math. Commun. 13(3), 421\u2013434 (2019)","journal-title":"Adv. Math. Commun."},{"key":"3230_CR20","volume-title":"Finite Rings with Identity","author":"BR McDonald","year":"1974","unstructured":"McDonald, B.R.: Finite Rings with Identity. Marcel Dekker, New York (1974)"},{"key":"3230_CR21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976667","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2010","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)"},{"key":"3230_CR22","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1142\/S0219749909005560","volume":"7","author":"J Qian","year":"2009","unstructured":"Qian, J., Ma, W., Gou, W.: Quantum codes from cyclic codes over finite rings. Int. J. Quant. Inf. 7, 1277\u20131283 (2009)","journal-title":"Int. J. Quant. Inf."},{"key":"3230_CR23","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.ffa.2014.11.005","volume":"33","author":"K Qian","year":"2015","unstructured":"Qian, K., Zhu, S., Kai, X.: On cyclic self-orthogonal codes over $${\\mathbb{Z}}_{2^m}$$. Finite Fields Appl. 33, 53\u201365 (2015)","journal-title":"Finite Fields Appl."},{"key":"3230_CR24","doi-asserted-by":"publisher","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. A 452, 2551\u20132577 (1996)","journal-title":"Proc. R. Soc. Lond. A"},{"key":"3230_CR25","doi-asserted-by":"publisher","first-page":"1701","DOI":"10.1109\/18.771249","volume":"45","author":"AM Steane","year":"1999","unstructured":"Steane, A.M.: Quantum Reed-Muller codes. IEEE Trans. Inf. Theory 45, 1701\u20131703 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3230_CR26","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"},{"key":"3230_CR27","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 reducung decoherence in quantum computer memory. Phys. Rev. A 52, 2493\u20132496 (1995)","journal-title":"Phys. Rev. A"},{"key":"3230_CR28","doi-asserted-by":"publisher","first-page":"4489","DOI":"10.1007\/s11128-016-1426-5","volume":"15","author":"Y Tang","year":"2016","unstructured":"Tang, Y., Zhu, S., Kai, X., Ding, J.: New quantum codes from dual-containing cyclic codes over finite rings. Quantum Inf. Process. 15, 4489\u20134500 (2016)","journal-title":"Quantum Inf. Process."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03230-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03230-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03230-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T02:55:21Z","timestamp":1633402521000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03230-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":28,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["3230"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03230-w","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2021,9]]},"assertion":[{"value":"12 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"303"}}