{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:36:31Z","timestamp":1764981391942,"version":"3.46.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2013,8,13]],"date-time":"2013-08-13T00:00:00Z","timestamp":1376352000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,9,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n                  <jats:p>In this paper, we study a special class of recently introduced\nquasigroups called multivariate quadratic quasigroups (MQQs) and\nsolve several open research problems about them.\nOur main contributions are threefold. The first\nis to provide a standard form of the MQQ generating function.\nSecondly, we show how to explicitly construct MQQs of higher orders and give\nlower bounds on the number of MQQs, which so far were open problems.\nLast, but not least, we refine the definition of MQQs of\ndifferent types by introducing the notion of \u201cMQQs of\nstrict type\u201d. The new concept has the advantage of being invariant\nunder invertible affine transformations over the set of the rows, columns and symbols of the multiplication table of an MQQ. It is therefore better suited to characterize\nthe complexity of the underneath multivariate quadratic system.<\/jats:p>","DOI":"10.1515\/jmc-2012-0006","type":"journal-article","created":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T16:11:38Z","timestamp":1376323898000},"page":"111-141","source":"Crossref","is-referenced-by-count":1,"title":["On a special class of multivariate quadratic quasigroups (MQQs)"],"prefix":"10.1515","volume":"7","author":[{"given":"Yanling","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Telematics, Norwegian University of Science and Technology, Norway"}]},{"given":"Danilo","family":"Gligoroski","sequence":"additional","affiliation":[{"name":"Department of Telematics, Norwegian University of Science and Technology, Norway"}]},{"given":"Svein J.","family":"Knapskog","sequence":"additional","affiliation":[{"name":"Q2S, Centre of Excellence, Norwegian University of Science and Technology, Norway"}]}],"member":"374","published-online":{"date-parts":[[2013,8,13]]},"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0006\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:32:40Z","timestamp":1764981160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0006\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,8,1]]},"published-print":{"date-parts":[[2013,9,1]]}},"alternative-id":["10.1515\/jmc-2012-0006"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2012-0006","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2013,8,13]]}}}