{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T20:31:02Z","timestamp":1770064262761,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171134, 62002093"],"award-info":[{"award-number":["12171134, 62002093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities of China","doi-asserted-by":"crossref","award":["JZ2022HGTB0264"],"award-info":[{"award-number":["JZ2022HGTB0264"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key Projects of Natural Science Research of Universities in Anhui Province","award":["KJ2021A1469"],"award-info":[{"award-number":["KJ2021A1469"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2024,11]]},"DOI":"10.1007\/s12095-024-00725-y","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T04:58:27Z","timestamp":1719896307000},"page":"1357-1381","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Several families of q-ary cyclic codes with length $$q^m-1$$"],"prefix":"10.1007","volume":"16","author":[{"given":"Jin","family":"Li","sequence":"first","affiliation":[]},{"given":"Huan","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Shan","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,1]]},"reference":[{"key":"725_CR1","doi-asserted-by":"publisher","first-page":"102308","DOI":"10.1016\/j.ffa.2023.102308","volume":"92","author":"T Chen","year":"2023","unstructured":"Chen, T., Ding, C., Li, C., Sun, Z.: Four infinite families of ternary cyclic codes with a square-root-like lower bound. Finite Fields Appl. 92, 102308 (2023)","journal-title":"Finite Fields Appl."},{"issue":"1","key":"725_CR2","doi-asserted-by":"publisher","first-page":"149","DOI":"10.3233\/FI-1999-381212","volume":"38","author":"C Ding","year":"1999","unstructured":"Ding, C., Lam, K., Xing, C.: Construction and enumeration of all binary duadic codes of length $$p^m$$. Fundam. Inform. 38(1), 149\u2013161 (1999)","journal-title":"Fundam. Inform."},{"issue":"2","key":"725_CR3","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1109\/18.748995","volume":"45","author":"C Ding","year":"1999","unstructured":"Ding, C., Pless, V.: Cyclotomy and duadic codes of prime lengths. IEEE Trans. Inform. Theory 45(2), 453\u2013466 (1999)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"725_CR4","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1109\/TIT.2004.839522","volume":"51","author":"P Gaborit","year":"2005","unstructured":"Gaborit, P., Nedeloaia, C.S., Wassermann, A.: On the weight enumerators of duadic and quadratic residue codes. IEEE Trans. Inform. Theory 51(1), 402\u2013407 (2005)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"725_CR5","unstructured":"Grassl, M.: Bounds on the minimum distance of linear codes and quantum codes. Online available at http:\/\/www.codetables.de"},{"key":"725_CR6","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":"5","key":"725_CR7","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1109\/TIT.1984.1056944","volume":"30","author":"JS Leon","year":"1984","unstructured":"Leon, J.S., Masley, J.M., Pless, V.: Duadic codes. IEEE Trans. Inform. Theory 30(5), 709\u2013714 (1984)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"5","key":"725_CR8","doi-asserted-by":"publisher","first-page":"1354","DOI":"10.1109\/18.21270","volume":"34","author":"JS Leon","year":"1988","unstructured":"Leon, J.S.: A probabilistic algorithm for computing minimum weight of large error-correcting codes. IEEE Trans. Inform. Theory 34(5), 1354\u20131359 (1988)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"725_CR9","doi-asserted-by":"publisher","first-page":"1910","DOI":"10.1016\/j.disc.2017.04.001","volume":"340","author":"H Liu","year":"2017","unstructured":"Liu, H., Ding, C., Li, C.: Dimensions of three types of BCH codes over $$GF(q)$$. Discret. Math. 340, 1910\u20131927 (2017)","journal-title":"Discret. Math."},{"key":"725_CR10","doi-asserted-by":"publisher","first-page":"102270","DOI":"10.1016\/j.ffa.2023.102270","volume":"91","author":"H Liu","year":"2023","unstructured":"Liu, H., Li, C., Ding, C.: Five infinite families of binary cyclic codes and their related codes with good parameters. Finite Fields Appl. 91, 102270 (2023)","journal-title":"Finite Fields Appl."},{"key":"725_CR11","doi-asserted-by":"crossref","unstructured":"Liu, H., Li, C., Qian, H.: Parameters of several families of binary duadic codes and their related codes. Des. Codes Crypt. 92, 1\u201312 (2024)","DOI":"10.1007\/s10623-023-01285-7"},{"key":"725_CR12","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. Amsterdam-New York-Oxford (1977)"},{"issue":"1","key":"725_CR13","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/0097-3165(87)90056-2","volume":"44","author":"V Pless","year":"1987","unstructured":"Pless, V., Masley, J.M., Leon, J.S.: On weights in duadic codes. J. Combin. Theory Ser. A 44(1), 6\u201321 (1987)","journal-title":"J. Combin. Theory Ser. A"},{"key":"725_CR14","unstructured":"Shi, M., Tao, S., Kim, J.L., Sol\u00e9, P.: A quaternary analogue of Tang-Ding codes. arXiv:2309.12003v1 (2023)"},{"key":"725_CR15","doi-asserted-by":"publisher","first-page":"102200","DOI":"10.1016\/j.ffa.2023.102200","volume":"89","author":"Z Sun","year":"2023","unstructured":"Sun, Z.: Several families of binary cyclic codes with good parameters. Finite Fields Appl. 89, 102200 (2023)","journal-title":"Finite Fields Appl."},{"key":"725_CR16","unstructured":"Sun, Z., Li, L., Zhu, S.: A Generalization of the Tang-Ding Binary Cyclic Codes. arXiv:2310.20179v1 (2023)"},{"issue":"1","key":"725_CR17","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.ffa.2009.11.003","volume":"16","author":"H Tada","year":"2010","unstructured":"Tada, H., Nishimura, S., Hiramatsu, T.: Cyclotomy and its application to duadic codes. Finite Fields Appl. 16(1), 4\u201313 (2010)","journal-title":"Finite Fields Appl."},{"issue":"12","key":"725_CR18","doi-asserted-by":"publisher","first-page":"7842","DOI":"10.1109\/TIT.2022.3193715","volume":"68","author":"C Tang","year":"2022","unstructured":"Tang, C., Ding, C.: Binary $$[n, (n + 1)\/2]$$ cyclic codes with good minimum distances. IEEE Trans. Inform. Theory 68(12), 7842\u20137849 (2022)","journal-title":"IEEE Trans. Inform. Theory"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00725-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-024-00725-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00725-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T16:08:48Z","timestamp":1737475728000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-024-00725-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,1]]},"references-count":18,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["725"],"URL":"https:\/\/doi.org\/10.1007\/s12095-024-00725-y","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,1]]},"assertion":[{"value":"8 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}