{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:48:17Z","timestamp":1767970097680,"version":"3.49.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T00:00:00Z","timestamp":1433376000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Key Basic Research Program of China","award":["2013CB834204"],"award-info":[{"award-number":["2013CB834204"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61171082"],"award-info":[{"award-number":["61171082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61301137"],"award-info":[{"award-number":["61301137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s12095-015-0140-y","type":"journal-article","created":{"date-parts":[[2015,6,3]],"date-time":"2015-06-03T21:51:08Z","timestamp":1433368268000},"page":"51-66","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Chinese remainder theorem approach to skew generalized quasi-cyclic codes over finite fields"],"prefix":"10.1007","volume":"8","author":[{"given":"Jian","family":"Gao","sequence":"first","affiliation":[]},{"given":"Linzhi","family":"Shen","sequence":"additional","affiliation":[]},{"given":"Fang-Wei","family":"Fu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,4]]},"reference":[{"key":"140_CR1","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1109\/TIT.2010.2044062","volume":"56","author":"T Abualrub","year":"2010","unstructured":"Abualrub, T., Aydin, N., Siap, I.: On the construction of skew quasi-cyclic codes. IEEE Trans. Inform. Theory 56, 2081\u20132090 (2010)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"140_CR2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10623-006-9034-5","volume":"42","author":"T Abualrub","year":"2007","unstructured":"Abualrub, T., Siap, I.: Cyclic codes over the ring \u2124 2 + u \u2124 2 $\\mathbb {Z}_{2}+u\\mathbb {Z}_{2}$ and \u2124 2 + u \u2124 2 + u 2 \u2124 2 $\\mathbb {Z}_{2} + u \\mathbb {Z}_{2} + u^{2} \\mathbb {Z}_{2}$ . Des. Codes Crypt. 42, 273\u2013287 (2007)","journal-title":"Des. Codes Crypt."},{"key":"140_CR3","doi-asserted-by":"crossref","first-page":"2065","DOI":"10.1109\/TIT.2002.1013145","volume":"48","author":"N Aydin","year":"2002","unstructured":"Aydin, N.: Quasi-cyclic codes over \u2124 4 $\\mathbb {Z}_{4}$ and some new binary codes. IEEE Trans. Inform. Theory 48, 2065\u20132069 (2002)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"140_CR4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s00200-009-0110-8","volume":"20","author":"M Bhaintwal","year":"2009","unstructured":"Bhaintwal, M., Wasan, S.: On quasi-cyclic codes over \u2124 q $\\mathbb {Z}_{q}$ . Appl. Algebra Eng. Commun. Comput. 20, 459\u2013480 (2009)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"140_CR5","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s10623-011-9494-0","volume":"62","author":"M Bhaintwal","year":"2012","unstructured":"Bhaintwal, M.: Skew quasi-cyclic codes over Galois rings. Des. Codes Crypt. 62, 85\u2013101 (2012)","journal-title":"Des. Codes Crypt."},{"key":"140_CR6","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00200-007-0043-z","volume":"18","author":"D Boucher","year":"2007","unstructured":"Boucher, D., Geisemann, W., Ulmer, F.: Skew-cyclic codes. Appl. Algebra Eng. Commun. Comput. 18, 379\u2013389 (2007)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"140_CR7","doi-asserted-by":"crossref","first-page":"273","DOI":"10.3934\/amc.2008.2.273","volume":"2","author":"D Boucher","year":"2008","unstructured":"Boucher, D., Sol\u00e9, P., Ulmer, F.: Skew constacyclic codes over Galois rings. Adv. Math. Commun. 2, 273\u2013292 (2008)","journal-title":"Adv. Math. Commun."},{"key":"140_CR8","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1016\/j.jsc.2007.11.008","volume":"44","author":"D Boucher","year":"2009","unstructured":"Boucher, D., Ulmer, F.: Coding with skew polynomial rings. J. Symbolic Comput. 44, 1644\u20131656 (2009)","journal-title":"J. Symbolic Comput."},{"key":"140_CR9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10623-010-9417-5","volume":"60","author":"Y Cao","year":"2011","unstructured":"Cao, Y.: Structural properties and enumeration of 1-generator generalized quasi-cyclic codes. Des. Codes Crypt. 60, 67\u201379 (2011)","journal-title":"Des. Codes Crypt."},{"key":"140_CR10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s00200-011-0145-5","volume":"22","author":"Y Cao","year":"2011","unstructured":"Cao, Y.: Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration. Appl. Algebra Eng. Commun. Comput. 22, 219\u2013233 (2011)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"140_CR11","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s10623-008-9230-6","volume":"50","author":"L Chaussade","year":"2009","unstructured":"Chaussade, L., Loidreau, P.: Skew codes of prescribed distance or rank. Des. Codes Crypt. 50, 267\u2013284 (2009)","journal-title":"Des. Codes Crypt."},{"key":"140_CR12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01270398","volume":"4","author":"J Conan","year":"1993","unstructured":"Conan, J., S\u00e9guin, G.: Structural properties and enumeration of quasi cyclic codes. Appl. Algebra Eng. Commun. Comput. 4, 25\u201339 (1993)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"140_CR13","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s00200-009-0095-3","volume":"20","author":"M Esmaeili","year":"2009","unstructured":"Esmaeili, M., Yari, S.: Generalized quasi-cyclic codes: structural properties and codes construction. Appl. Algebra Eng. Commun. Comput. 20, 159\u2013173 (2009)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"140_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02429-0","volume-title":"Finite Dimensional Division Algebras over Fields","author":"N Jacobson","year":"1996","unstructured":"Jacobson, N: Finite Dimensional Division Algebras over Fields. Springer, New York (1996)"},{"key":"140_CR15","doi-asserted-by":"crossref","unstructured":"Lally, K.: Quasicyclic codes of index l over F q $\\mathbb {F}_{q}$ viewed as F q [ x ] $\\mathbb {F}_{q}[x]$ -submodules of F q l [ x ] \/ ( x m \u2212 1 ) $\\mathbb {F}_{q^{l}}[x]\/(x^{m}-1)$ . In: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Comput. Sci. 2643, Springer-Verlag, Berlin, Heidelberg, 244-253 (2003)","DOI":"10.1007\/3-540-44828-4_26"},{"key":"140_CR16","doi-asserted-by":"crossref","first-page":"2751","DOI":"10.1109\/18.959257","volume":"47","author":"S Ling","year":"2001","unstructured":"Ling, S., Sol\u00e9, P.: On the algebra structure of quasi-cyclic codes I: finite fields. IEEE Trans. Inform. Theory 47, 2751\u20132760 (2001)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"140_CR17","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1023\/A:1024715527805","volume":"30","author":"S Ling","year":"2003","unstructured":"Ling, S., Sol\u00e9, P.: On the algebra structure of quasi-cyclic codes II: chain rings. Des. Codes Crypt. 30(1), 113\u2013130 (2003)","journal-title":"Des. Codes Crypt."},{"key":"140_CR18","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1109\/TIT.2005.850142","volume":"51","author":"S Ling","year":"2005","unstructured":"Ling, S., Sol\u00e9, P.: On the algebra structure of quasi-cyclic codes III: generator theory. IEEE Trans. Inform. Theory 51, 2692\u20132700 (2005)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"140_CR19","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":"140_CR20","first-page":"24","volume":"5","author":"I Siap","year":"2005","unstructured":"Siap, I., Kulhan, N.: The structure of generalized quasi-cyclic codes. Appl. Math. E-Notes 5, 24\u201330 (2005)","journal-title":"Appl. Math. E-Notes"},{"key":"140_CR21","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.jfranklin.2011.10.020","volume":"349","author":"I Siap","year":"2012","unstructured":"Siap, I., Abualrub, T., Yildiz, B.: One generator quasi-cyclic codes over F 2 + u F 2 $\\mathbb {F}_{2}+u\\mathbb {F}_{2}$ . J. Frank. Inst. 349, 284\u2013292 (2012)","journal-title":"J. Frank. Inst."}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-015-0140-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12095-015-0140-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-015-0140-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,25]],"date-time":"2019-08-25T22:52:17Z","timestamp":1566773537000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12095-015-0140-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,4]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["140"],"URL":"https:\/\/doi.org\/10.1007\/s12095-015-0140-y","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,4]]}}}