{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T03:14:06Z","timestamp":1772766846088,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T00:00:00Z","timestamp":1588723200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T00:00:00Z","timestamp":1588723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s00200-020-00434-y","type":"journal-article","created":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T23:19:52Z","timestamp":1588720792000},"page":"73-89","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Euclidean self-dual codes and isometry codes"],"prefix":"10.1007","volume":"33","author":[{"given":"Lin","family":"Sok","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,5,6]]},"reference":[{"issue":"5","key":"434_CR1","doi-asserted-by":"publisher","first-page":"2051","DOI":"10.1109\/18.930940","volume":"47","author":"KT Arasu","year":"2001","unstructured":"Arasu, K.T., Gulliver, T.A.: Self-dual codes over $$\\mathbb{F}_p$$ and weighing matrices. IEEE Trans. Inf. Theory 47(5), 2051\u20132056 (2001)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"434_CR2","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0012-365X(02)00520-4","volume":"262","author":"K Betsumiya","year":"2003","unstructured":"Betsumiya, K., Georgiou, S., Gulliver, T.A., Harada, M., Koukouvinos, C.: On self-dual codes over some prime fields. Discrete Math. 262, 37\u201358 (2003)","journal-title":"Discrete Math."},{"key":"434_CR3","unstructured":"Bosma, W., Cannon, J.J., Fieker, C., Steel, A.(eds.): Handbook of Magma Functions, Edition 2.16, 5017 p (2010)"},{"issue":"5","key":"434_CR4","doi-asserted-by":"publisher","first-page":"2055","DOI":"10.1109\/18.930941","volume":"47","author":"H Chen","year":"2001","unstructured":"Chen, H., Ling, S., Xing, C.P.: Asymptotically good quantum codes exceeding the Ashikhmin\u2013Litsyn\u2013Tsfasman bound. IEEE Trans. Inf. Theory 47(5), 2055\u20132058 (2001)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"434_CR5","doi-asserted-by":"publisher","first-page":"2647","DOI":"10.1109\/TIT.2008.921692","volume":"54","author":"R Cramer","year":"2008","unstructured":"Cramer, R., Daza, V., Gracia, I., Urroz, J.J., Leander, G., Marti-Farre, J., Padro, C.: On codes, matroids, and secure multiparty computation from linear secret-sharing schemes. IEEE Trans. Inf. Theory 54(6), 2647\u20132657 (2008)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"434_CR6","doi-asserted-by":"crossref","unstructured":"Dougherty, S.T., Mesnager, S., Sol\u00e9, P.: Secret-sharing schemes based on self-dual codes. In: IEEE Information Theory Workshop, pp. 338\u2013342 (2008)","DOI":"10.1109\/ITW.2008.4578681"},{"issue":"9","key":"434_CR7","doi-asserted-by":"publisher","first-page":"5574","DOI":"10.1109\/TIT.2019.2916367","volume":"65","author":"W Fang","year":"2019","unstructured":"Fang, W., Fu, F.: New constructions of MDS Euclidean self-dual codes from GRS codes and extended GRS codes. IEEE Trans. Inf. Theory 65(9), 5574\u20135579 (2019)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"434_CR8","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1006\/jcta.2001.3198","volume":"97","author":"P Gaborit","year":"2002","unstructured":"Gaborit, P.: Quadratic double circulant codes over fields. J. Combin. Theory A 97(1), 85\u2013107 (2002)","journal-title":"J. Combin. Theory A"},{"key":"434_CR9","unstructured":"Gaborit, P.: Table of self-dual codes over $${\\mathbb{F}} _4$$ (2020). http:\/\/www.unilim.fr\/pages_perso\/philippe.gaborit\/SD\/GF4E\/GF4E.htm. Accessed 07 March 2020"},{"issue":"3","key":"434_CR10","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/S1071-5797(03)00011-X","volume":"9","author":"P Gaborit","year":"2003","unstructured":"Gaborit, P., Otmani, A.: Experimental constructions of self-dual codes. Finite Fields Appl. 9(3), 372\u2013394 (2003)","journal-title":"Finite Fields Appl."},{"key":"434_CR11","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/S1071-5797(02)90353-9","volume":"8","author":"S Georgiou","year":"2002","unstructured":"Georgiou, S., Koukouvinos, C.: MDS self-dual codes over large prime fields. Finite Fields Appl. 8, 455\u2013470 (2002)","journal-title":"Finite Fields Appl."},{"key":"434_CR12","unstructured":"Grassl, M.: Table of best known linear codes (2020). http:\/\/www.codetables.de\/. Accessed 07 March 2020"},{"key":"434_CR13","doi-asserted-by":"crossref","unstructured":"Grassl, M., Gulliver, T. A.: On self-dual MDS codes. In: ISIT 2008 Toronto, Canada, July 6 \u201311 (2008)","DOI":"10.1109\/ISIT.2008.4595330"},{"key":"434_CR14","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10623-011-9489-x","volume":"62","author":"K Guenda","year":"2012","unstructured":"Guenda, K.: New MDS self-dual codes over finite fields. Des. Codes Crypt. 62, 31\u201342 (2012)","journal-title":"Des. Codes Crypt."},{"issue":"3","key":"434_CR15","doi-asserted-by":"publisher","first-page":"1434","DOI":"10.1109\/TIT.2016.2645759","volume":"63","author":"LF Jin","year":"2017","unstructured":"Jin, L.F., Xing, C.P.: New MDS self-dual codes from generalized Reed\u2013Solomon codes. IEEE Trans. Inf. Theory 63(3), 1434\u20131438 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"434_CR16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10623-007-9117-y","volume":"45","author":"J-L Kim","year":"2007","unstructured":"Kim, J.-L., Lee, Y.: Construction of MDS self-dual codes over Galois rings. Des. Codes Crypt. 45, 247\u2013258 (2007)","journal-title":"Des. Codes Crypt."},{"key":"434_CR17","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.jcta.2003.10.003","volume":"105","author":"J-L Kim","year":"2004","unstructured":"Kim, J.-L., Lee, Y.: Euclidean and Hermitian self-dual MDS codes over large finite fields. J. Combin. Theory Ser. A 105, 79\u201395 (2004)","journal-title":"J. Combin. Theory Ser. A"},{"key":"434_CR18","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1080\/00029890.1969.12000160","volume":"76","author":"FJ MacWilliams","year":"1969","unstructured":"MacWilliams, F.J.: Orthogonal matrices over finite fields. Am. Math. Mon. 76, 152\u2013164 (1969)","journal-title":"Am. Math. Mon."},{"key":"434_CR19","volume-title":"The Theory of Error-Correcting Codes","author":"FJ MacWilliams","year":"1977","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)"},{"key":"434_CR20","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/0012-365X(72)90030-1","volume":"3","author":"FJ MacWilliams","year":"1972","unstructured":"MacWilliams, F.J., Sloane, N.J.A., Thompson, J.G.: Good self-dual codes exist. Discrete Math. 3, 153\u2013162 (1972)","journal-title":"Discrete Math."},{"key":"434_CR21","unstructured":"Massey, J.: Some applications of coding theory in cryptography. In: Proceedings of 4th IMA conference on cryptography and coding, pp. 33\u201347 (1995)"},{"key":"434_CR22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2954877","author":"L Sok","year":"2019","unstructured":"Sok, L.: Explicit constructions of MDS self-dual codes. IEEE Trans. Inf. Theory (2019). https:\/\/doi.org\/10.1109\/TIT.2019.2954877","journal-title":"IEEE Trans. Inf. Theory"},{"key":"434_CR23","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/j.ffa.2018.08.011","volume":"54","author":"M Shi","year":"2018","unstructured":"Shi, M., Sok, L., Sol\u00e9, P., \u00c7alkavur, S.: Self-dual codes and orthogonal matrices over large finite fields. Finite Fields Appl. 54, 297\u2013314 (2018)","journal-title":"Finite Fields Appl."},{"key":"434_CR24","volume-title":"The Geometry of the Classical Groups Sigma Series in Pure Mathematics 9","author":"D Taylor","year":"1992","unstructured":"Taylor, D.: The Geometry of the Classical Groups Sigma Series in Pure Mathematics 9. Heldermann Verlag, Berlin (1992)"},{"key":"434_CR25","doi-asserted-by":"publisher","first-page":"325","DOI":"10.4236\/apm.2017.75019","volume":"7","author":"H Tong","year":"2017","unstructured":"Tong, H., Wang, X.: New MDS Euclidean and Hermitian self-dual codes over finite fields. Adv. Pure Math. 7, 325\u2013333 (2017)","journal-title":"Adv. Pure Math."},{"key":"434_CR26","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s12095-018-0288-3","volume":"11","author":"H Yan","year":"2019","unstructured":"Yan, H.: A note on the constructions of MDS self-dual codes. Cryptogr. Commun. 11, 259\u2013268 (2019)","journal-title":"Cryptogr. Commun."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-020-00434-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-020-00434-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-020-00434-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,20]],"date-time":"2022-01-20T18:03:26Z","timestamp":1642701806000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-020-00434-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,6]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["434"],"URL":"https:\/\/doi.org\/10.1007\/s00200-020-00434-y","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,6]]},"assertion":[{"value":"20 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The author would like to declare that no conflict of interest exits in the submission of this manuscript, and manuscript is an original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}