{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T23:40:05Z","timestamp":1749512405751,"version":"3.41.0"},"reference-count":8,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T00:00:00Z","timestamp":1698883200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T00:00:00Z","timestamp":1698883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s00200-023-00634-2","type":"journal-article","created":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T08:02:09Z","timestamp":1698912129000},"page":"715-730","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Using elliptic curves to construct 3D arrays"],"prefix":"10.1007","volume":"36","author":[{"given":"Alcib\u00edades","family":"Bustillo-Z\u00e1rate","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dorothy","family":"Bollman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Ortiz-Ubarri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,2]]},"reference":[{"key":"634_CR1","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s00200-019-00393-z","volume":"31","author":"R Arce-Nazario","year":"2020","unstructured":"Arce-Nazario, R., Castro, F., Gomez-Perez, D., Moreno, O., Ortiz-Ubarri, J., Rubio, I., Tirkel, A.: Multidimensional linear complexity analysis of periodic arrays. Appl. Algebra Eng. Commun. Comput. 31, 43\u201363 (2020)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"634_CR2","doi-asserted-by":"publisher","first-page":"313","DOI":"10.3934\/amc.2017024","volume":"11","author":"D Gomez-Perez","year":"2017","unstructured":"Gomez-Perez, D., Gomez, A., Tirkel, A.: Arrays composed from the extended rational cycle. Adv. Math. Commun. 11, 313\u2013327 (2017)","journal-title":"Adv. Math. Commun."},{"doi-asserted-by":"crossref","unstructured":"Rubio, I.M., Sweedler, M., Heegard, C.: Finding a Gr\u00f6bner basis for the ideal of recurrence relations on m-dimensional periodic arrays. In: Contemporary Developments in Finite Fields and Applications, pp. 296\u2013320 (2016)","key":"634_CR3","DOI":"10.1142\/9789814719261_0018"},{"doi-asserted-by":"crossref","unstructured":"Blake, S., Moreno, O., Tirkel, A.: Families of 3D Arrays for Video Watermarking. In: Sequences and Their Applications - SETA 2014, vol. 8865, pp. 134\u2013145. Springer, Cham (2014)","key":"634_CR4","DOI":"10.1007\/978-3-319-12325-7_12"},{"doi-asserted-by":"crossref","unstructured":"Moreno, O., Tirkel, A.: Multi-dimensional arrays for watermarking. In: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 2691\u20132695 (2011)","key":"634_CR5","DOI":"10.1109\/ISIT.2011.6034060"},{"key":"634_CR6","first-page":"246","volume-title":"Understanding Cryptography: A Textbook for Students and Practitioners","author":"C Paar","year":"2009","unstructured":"Paar, C., Pelzl, J.: Understanding Cryptography: A Textbook for Students and Practitioners, 1st edn., p. 246. Springer, Berlin (2009)","edition":"1"},{"issue":"5","key":"634_CR7","doi-asserted-by":"publisher","first-page":"3237","DOI":"10.1109\/TIT.2013.2237754","volume":"59","author":"X Zeng","year":"2013","unstructured":"Zeng, X., Cai, H., Tang, X., Yang, Y.: Optimal frequency hopping sequences of odd length. IEEE Trans. Inf. Theory 59(5), 3237\u20133248 (2013). https:\/\/doi.org\/10.1109\/TIT.2013.2237754","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"634_CR8","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1109\/TIT.1974.1055219","volume":"20","author":"L Welch","year":"1974","unstructured":"Welch, L.: Lower bounds on the maximum cross correlation of signals (Corresp.). IEEE Trans. Inf. Theory 20(3), 397\u2013399 (1974). https:\/\/doi.org\/10.1109\/TIT.1974.1055219","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-023-00634-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-023-00634-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-023-00634-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T23:02:12Z","timestamp":1749510132000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-023-00634-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,2]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["634"],"URL":"https:\/\/doi.org\/10.1007\/s00200-023-00634-2","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"type":"print","value":"0938-1279"},{"type":"electronic","value":"1432-0622"}],"subject":[],"published":{"date-parts":[[2023,11,2]]},"assertion":[{"value":"14 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2023","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 that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}