{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T22:42:01Z","timestamp":1781476921725,"version":"3.54.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"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":["12301670"],"award-info":[{"award-number":["12301670"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin","doi-asserted-by":"crossref","award":["23JCQNJC00050"],"award-info":[{"award-number":["23JCQNJC00050"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10623-025-01668-y","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T15:08:36Z","timestamp":1758294516000},"page":"5423-5444","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New constructions of cyclic constant-dimension subspace codes based on Sidon spaces and subspace polynomials"],"prefix":"10.1007","volume":"93","author":[{"given":"Gang","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"You","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,19]]},"reference":[{"issue":"4","key":"1668_CR1","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1109\/18.850663","volume":"46","author":"R Ahlswede","year":"2000","unstructured":"Ahlswede R., Cai N., Li S., Yeung R.W.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204\u20131216 (2000).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"1668_CR2","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1017\/S0305004117000044","volume":"163","author":"C Bachoc","year":"2017","unstructured":"Bachoc C., Serra O., Z\u00e9mor G.: An analogue of Vosper\u2019s theorem for extension fields. Math. Proc. Camb. Philos. Soc. 163(3), 423\u2013452 (2017).","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"3","key":"1668_CR3","first-page":"611","volume":"93","author":"D Bartoli","year":"2025","unstructured":"Bartoli D., Ghiandoni S.: Algebraic\u2013geometric analysis of three-dimensional maximum rank distance codes. Des. Codes Cryptogr. 93(3), 611\u2013631 (2025).","journal-title":"Des. Codes Cryptogr."},{"issue":"3","key":"1668_CR4","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1109\/TIT.2016.2520479","volume":"62","author":"E Ben-Sasson","year":"2016","unstructured":"Ben-Sasson E., Etzion T., Gabizon A., Raviv N.: Subspace polynomials and cyclic subspace codes. IEEE Trans. Inf. Theory 62(3), 1157\u20131165 (2016).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"1668_CR5","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1109\/TIT.2009.2034780","volume":"56","author":"E Ben-Sasson","year":"2010","unstructured":"Ben-Sasson E., Kopparty S., Radhakrishnan J.: Subspace polynomials and limits to list decoding of Reed\u2013Solomon codes. IEEE Trans. Inf. Theory 56(1), 113\u2013120 (2010).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"e7","key":"1668_CR6","first-page":"1","volume":"4","author":"M Braun","year":"2016","unstructured":"Braun M., Etzion T., Ostergard P., Vardy A., Wassermann A.: Existence of $$q$$-analogs of Steiner systems. Forum Math. Pi 4(e7), 1\u201314 (2016).","journal-title":"Forum Math. Pi"},{"key":"1668_CR7","unstructured":"Cai N., Yeung R.W.: Network coding and error correction. In: Proceedings of the IEEE information theory workshop, pp. 119\u2013122 (2002)."},{"issue":"6","key":"1668_CR8","doi-asserted-by":"publisher","first-page":"1267","DOI":"10.1007\/s10623-017-0394-9","volume":"86","author":"B Chen","year":"2018","unstructured":"Chen B., Liu H.: Constructions of cyclic constant dimension codes. Des. Codes Cryptogr. 86(6), 1267\u20131279 (2018).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1668_CR9","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1109\/TIT.2010.2095232","volume":"57","author":"T Etzion","year":"2011","unstructured":"Etzion T., Vardy A.: Error-correcting codes in projective space. IEEE Trans. Inf. Theory 57(2), 1165\u20131173 (2011).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"1668_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2020.112273","volume":"344","author":"T Feng","year":"2021","unstructured":"Feng T., Wang Y.: New constructions of large cyclic subspace codes and Sidon spaces. Discret. Math. 344(4), 112273 (2021).","journal-title":"Discret. Math."},{"issue":"3","key":"1668_CR11","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/s10623-020-00823-x","volume":"89","author":"H Gluesing-Luerssen","year":"2021","unstructured":"Gluesing-Luerssen H., Hunter L.: Distance distributions of cyclic orbit codes. Des. Codes Cryptogr. 89(3), 447\u2013470 (2021).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1668_CR12","doi-asserted-by":"publisher","first-page":"177","DOI":"10.3934\/amc.2015.9.177","volume":"9","author":"H Gluesing-Luerssen","year":"2015","unstructured":"Gluesing-Luerssen H., Morrison K., Troha C.: Cyclic orbit codes and stabilizer subfields. Adv. Math. Commun. 9(2), 177\u2013197 (2015).","journal-title":"Adv. Math. Commun."},{"issue":"10","key":"1668_CR13","doi-asserted-by":"publisher","first-page":"4413","DOI":"10.1109\/TIT.2006.881746","volume":"52","author":"T Ho","year":"2006","unstructured":"Ho T., M\u00e9dard M., Koetter R., Karger D.R., Effros M., Shi J., Leong B.: A random linear network coding approach to multicast. IEEE Trans. Inf. Theory 52(10), 4413\u20134430 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"1668_CR14","doi-asserted-by":"publisher","first-page":"3579","DOI":"10.1109\/TIT.2008.926449","volume":"54","author":"R Koetter","year":"2008","unstructured":"Koetter R., Kschischang F.: Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54(8), 3579\u20133591 (2008).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1668_CR15","doi-asserted-by":"crossref","unstructured":"Koetter R., M\u00e9dard M.: Beyond routing: an algebraic approach to network coding, In: Proceedings of twenty-first annual joint conference of the IEEE Comput. and Commun. Soc., pp. 122\u2013130 (2002).","DOI":"10.1109\/INFCOM.2002.1019253"},{"key":"1668_CR16","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-3-540-89994-5_4","volume":"5393","author":"A Kohnert","year":"2008","unstructured":"Kohnert A., Kurz S.: Construction of large constant dimension codes with a prescribed minimum distance. Math. Methods Comput. Sci. 5393, 31\u201342 (2008).","journal-title":"Math. Methods Comput. Sci."},{"issue":"4","key":"1668_CR17","doi-asserted-by":"publisher","first-page":"956","DOI":"10.3934\/amc.2022039","volume":"18","author":"H Lao","year":"2022","unstructured":"Lao H., Chen H.: New constant dimension subspace codes from multilevel linkage construction. Adv. Math. Commun. 18(4), 956\u2013966 (2022).","journal-title":"Adv. Math. Commun."},{"issue":"4","key":"1668_CR18","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1007\/s10623-022-01146-9","volume":"91","author":"Y Li","year":"2023","unstructured":"Li Y., Liu H.: Cyclic constant dimension subspace codes via the sum of Sidon spaces. Des. Codes Cryptogr. 91(4), 1193\u20131207 (2023).","journal-title":"Des. Codes Cryptogr."},{"issue":"5","key":"1668_CR19","doi-asserted-by":"publisher","first-page":"1423","DOI":"10.1007\/s10623-023-01350-1","volume":"92","author":"Y Li","year":"2024","unstructured":"Li Y., Liu H., Mesnager S.: New constructions of constant dimension subspace codes with large sizes. Des. Codes Cryptogr. 92(5), 1423\u20131437 (2024).","journal-title":"Des. Codes Cryptogr."},{"key":"1668_CR20","volume-title":"Finite fields","author":"R Lidl","year":"1997","unstructured":"Lidl R., Niederreiter H.: Finite fields. Cambridge University Press, Cambridge (1997)."},{"key":"1668_CR21","doi-asserted-by":"crossref","unstructured":"Liu X., Shi T., Niu M., Shen L., Gao Y.: New constructions of Sidon spaces and cyclic subspace codes. In: IEICE on Fundamentals of Electronics Communications and Computer Sciences, E106-A(8), pp. 1062\u20131066 (2023).","DOI":"10.1587\/transfun.2022EAL2074"},{"key":"1668_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2022.102045","volume":"81","author":"A Neri","year":"2022","unstructured":"Neri A., Santonastaso P., Zullo F.: Extending two families of maximum rank distance codes. Finite Fields Appl. 81, 102045 (2022).","journal-title":"Finite Fields Appl."},{"issue":"4","key":"1668_CR23","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.3934\/amc.2022074","volume":"18","author":"M Niu","year":"2022","unstructured":"Niu M., Xiao J., Gao Y.: New constructions of large cyclic subspace codes via Sidon spaces. Adv. Math. Commun. 18(4), 1123\u20131137 (2022).","journal-title":"Adv. Math. Commun."},{"issue":"5","key":"1668_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2019.111788","volume":"343","author":"Y Niu","year":"2020","unstructured":"Niu Y., Yue Q., Wu Y.: Several kinds of large cyclic subspace codes via Sidon spaces. Discret. Math. 343(5), 111788 (2020).","journal-title":"Discret. Math."},{"issue":"2","key":"1668_CR25","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s10623-016-0297-1","volume":"85","author":"K Otal","year":"2017","unstructured":"Otal K., \u00d6zbudak F.: Cyclic subspace codes via subspace polynomials. Des. Codes Cryptogr. 85(2), 191\u2013204 (2017).","journal-title":"Des. Codes Cryptogr."},{"issue":"6","key":"1668_CR26","doi-asserted-by":"publisher","first-page":"4412","DOI":"10.1109\/TIT.2017.2766178","volume":"64","author":"RM Roth","year":"2017","unstructured":"Roth R.M., Raviv N., Tamo I.: Construction of Sidon spaces with applications to coding. IEEE Trans. Inf. Theory 64(6), 4412\u20134422 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"1668_CR27","doi-asserted-by":"publisher","first-page":"7386","DOI":"10.1109\/TIT.2013.2274266","volume":"59","author":"AL Trautmann","year":"2013","unstructured":"Trautmann A.L., Manganiello F., Braun M., Rosenthal J.: Cyclic orbit codes. IEEE Trans. Inf. Theory 59(11), 7386\u20137404 (2013).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"1668_CR28","doi-asserted-by":"publisher","first-page":"3799","DOI":"10.1007\/s10623-024-01466-y","volume":"92","author":"S Yu","year":"2024","unstructured":"Yu S., Ji L.: Two new constructions of cyclic subspace codes via Sidon spaces. Des. Codes Cryptogr. 92(11), 3799\u20133811 (2024).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1668_CR29","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s12095-020-00463-x","volume":"13","author":"H Zhang","year":"2021","unstructured":"Zhang H., Cao X.: Further constructions of cyclic subspace codes. Cryptogr. Commun. 13(2), 245\u2013262 (2021).","journal-title":"Cryptogr. Commun."},{"issue":"2","key":"1668_CR30","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s11464-022-1011-4","volume":"17","author":"H Zhang","year":"2022","unstructured":"Zhang H., Cao X.: Constructions of Sidon spaces and cyclic subspace codes. Front. Math. China 17(2), 275\u2013288 (2022).","journal-title":"Front. Math. China"},{"issue":"1","key":"1668_CR31","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10623-022-01095-3","volume":"91","author":"H Zhang","year":"2023","unstructured":"Zhang H., Tang C.: Constructions of large cyclic constant dimension codes via Sidon spaces. Des. Codes Cryptogr. 91(1), 29\u201344 (2023).","journal-title":"Des. Codes Cryptogr."},{"key":"1668_CR32","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.laa.2022.12.011","volume":"661","author":"H Zhang","year":"2023","unstructured":"Zhang H., Tang C.: Further constructions of large cyclic subspace codes via Sidon spaces. Linear Algebra Appl. 661, 106\u2013115 (2023).","journal-title":"Linear Algebra Appl."},{"issue":"5","key":"1668_CR33","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1007\/s40314-023-02353-3","volume":"42","author":"H Zhang","year":"2023","unstructured":"Zhang H., Tang C., Hu X.: New constructions of Sidon spaces and large cyclic constant dimension codes. Comput. Appl. Math. 42(5), 230 (2023).","journal-title":"Comput. Appl. Math."},{"issue":"3","key":"1668_CR34","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/s10801-021-01069-z","volume":"55","author":"T Zhang","year":"2022","unstructured":"Zhang T., Ge G.: New constructions of Sidon spaces. J. Algebraic Combin. 55(3), 781\u2013794 (2022).","journal-title":"J. Algebraic Combin."},{"key":"1668_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ffa.2019.01.002","volume":"57","author":"W Zhao","year":"2019","unstructured":"Zhao W., Tang X.: A characterization of cyclic subspace codes via subspace polynomials. Finite Fields Appl. 57, 1\u201312 (2019).","journal-title":"Finite Fields Appl."},{"key":"1668_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2022.102153","volume":"87","author":"F Zullo","year":"2023","unstructured":"Zullo F.: Multi-orbit cyclic subspace codes and linear sets. Finite Fields Appl. 87, 102153 (2023).","journal-title":"Finite Fields Appl."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01668-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01668-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01668-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T15:18:27Z","timestamp":1763997507000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01668-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,19]]},"references-count":36,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["1668"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01668-y","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,19]]},"assertion":[{"value":"18 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 September 2025","order":4,"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 no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}