{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T14:48:37Z","timestamp":1772808517712,"version":"3.50.1"},"reference-count":21,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2016]]},"DOI":"10.3934\/amc.2016006","type":"journal-article","created":{"date-parts":[[2016,5,2]],"date-time":"2016-05-02T17:06:13Z","timestamp":1462208773000},"page":"291-306","source":"Crossref","is-referenced-by-count":0,"title":["Constructing commutative semifields of square order"],"prefix":"10.3934","volume":"10","author":[{"given":"Stephen M.","family":"Gagola III","sequence":"first","affiliation":[]},{"given":"Joanne L.","family":"Hall","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2016006-1","doi-asserted-by":"publisher","unstructured":"A. A. Albert, Quasigroups I, <em>Trans. Amer. Math. Soc.<\/em>, <strong>54<\/strong> (1943), 507-519.","DOI":"10.2307\/1990259"},{"key":"key-10.3934\/amc.2016006-2","doi-asserted-by":"publisher","unstructured":"J. Bierbrauer, Commutative semifields from projection mappings, <em>Des. Codes Crypt.<\/em>, <strong>61<\/strong> (2011), 187-196.","DOI":"10.1007\/s10623-010-9447-z"},{"key":"key-10.3934\/amc.2016006-3","doi-asserted-by":"publisher","unstructured":"A. Blokhuis, R. S. Coulter, M. Henderson and C. M. O'Keefe, Permutations amongst the Dembowski-Ostrom polynomials, in <em>Finite Fields and Applications<\/em>, Springer, 2001, 37-42.","DOI":"10.1007\/978-3-642-56755-1_4"},{"key":"key-10.3934\/amc.2016006-4","doi-asserted-by":"publisher","unstructured":"L. Budaghyan and T. Helleseth, New commutative semifields defined by new PN multinomials, <em>Crypt. Commun.<\/em>, <strong>3<\/strong> (2011), 1-16.","DOI":"10.1007\/s12095-010-0022-2"},{"key":"key-10.3934\/amc.2016006-5","doi-asserted-by":"publisher","unstructured":"L. Budaghyan and T. Helleseth, On isotopisms of commutative presemifields and CCZ-equivalence of functions, <em>Int. J. Found. Comput. Sci.<\/em>, <strong>22<\/strong> (2011), 1243-1258.","DOI":"10.1142\/S0129054111008684"},{"key":"key-10.3934\/amc.2016006-6","doi-asserted-by":"publisher","unstructured":"C. Carlet, P. Charpin and V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptosystems, <em>Des. Codes Crypt.<\/em>, <strong>15<\/strong> (1998), 125-156.","DOI":"10.1023\/A:1008344232130"},{"key":"key-10.3934\/amc.2016006-7","doi-asserted-by":"publisher","unstructured":"C. Carlet and C. Ding, Highly nonlinear mappings, <em>J. Complexity<\/em>, <strong>20<\/strong> (2004), 205-244.","DOI":"10.1016\/j.jco.2003.08.008"},{"key":"key-10.3934\/amc.2016006-8","doi-asserted-by":"publisher","unstructured":"R. S. Coulter and M. Henderson, Commutative presemifields and semifields, <em>Adv. Math.<\/em>, <strong>217<\/strong> (2008), 282-304, 2008.","DOI":"10.1016\/j.aim.2007.07.007"},{"key":"key-10.3934\/amc.2016006-9","doi-asserted-by":"publisher","unstructured":"R. S. Coulter and R. W. Matthews, Planar functions and planes of Lenz-Barlotti class II, <em>Des. Codes Crypt.<\/em>, <strong>10<\/strong> (1997), 167-184.","DOI":"10.1023\/A:1008292303803"},{"key":"key-10.3934\/amc.2016006-10","unstructured":"T. W. Cusick, C. Ding and A. R. Renvall, <em>Stream Ciphers and Number Theory<\/em>, Elsevier, 2004."},{"key":"key-10.3934\/amc.2016006-11","doi-asserted-by":"publisher","unstructured":"P. Dembowski and T. G. Ostrom, Planes of order $n$ with collineation groups of order $n^2$, <em>Math. Z.<\/em>, <strong>103<\/strong> (1968), 239-258.","DOI":"10.1007\/BF01111042"},{"key":"key-10.3934\/amc.2016006-12","doi-asserted-by":"publisher","unstructured":"C. Ding and J. Yin, Signal sets from functions with optimum nonlinearity, <em>IEEE Trans. Commun.<\/em>, <strong>55<\/strong> (2007), 936-940.","DOI":"10.1109\/TCOMM.2007.894113"},{"key":"key-10.3934\/amc.2016006-13","unstructured":"The GAP Group, GAP - Groups, Algorithms and Programming, Version 4.5.5, 2012."},{"key":"key-10.3934\/amc.2016006-14","doi-asserted-by":"crossref","unstructured":"K. J. Horadam, <em>Hadamard Matrices and their Applications<\/em>, Princeton Univ. Press, Princeton, 2007.","DOI":"10.1515\/9781400842902"},{"key":"key-10.3934\/amc.2016006-15","doi-asserted-by":"publisher","unstructured":"W. Jia, X. Zeng, T. Helleseth and C. Li, A class of binomial bent functions over the finite fields of odd characteristic, <em>IEEE Trans. Inf. Theory<\/em>, <strong>58<\/strong> (2012), 6054-6063.","DOI":"10.1109\/TIT.2012.2199736"},{"key":"key-10.3934\/amc.2016006-16","doi-asserted-by":"publisher","unstructured":"D. E. Knuth, Finite semifields and projective planes, <em>J. Algebra<\/em>, <strong>2<\/strong> (1965), 182-217.","DOI":"10.1016\/0021-8693(65)90018-9"},{"key":"key-10.3934\/amc.2016006-17","doi-asserted-by":"publisher","unstructured":"G. Kyureghyan and A. Pott, Some theorems on planar mappings, in <em>Arithmetic of Finite Fields<\/em>, Springer, Berlin, 2008, 117-122.","DOI":"10.1007\/978-3-540-69499-1_10"},{"key":"key-10.3934\/amc.2016006-18","doi-asserted-by":"publisher","unstructured":"G. Marino and O. Polverino, On the nuclei of a finite semifield, <em>Theory Appl. Finite Fields. Contemp. Math.<\/em>, <strong>579<\/strong> (2012), 123-141.","DOI":"10.1090\/conm\/579\/11525"},{"key":"key-10.3934\/amc.2016006-19","doi-asserted-by":"publisher","unstructured":"A. Roy and A. J. Scott, Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements, <em>J. Math. Phys.<\/em>, <strong>48<\/strong> (2007), 1-24.","DOI":"10.1063\/1.2748617"},{"key":"key-10.3934\/amc.2016006-20","doi-asserted-by":"publisher","unstructured":"J. Wedderburn, A theorem on finite algebras, <em>Trans. Amer. Math. Soc.<\/em>, <strong>6<\/strong> (1903), 349-352.","DOI":"10.2307\/1986226"},{"key":"key-10.3934\/amc.2016006-21","doi-asserted-by":"publisher","unstructured":"Y. Zhou and A. Pott, A new family of semifields with 2 parameters, <em>Adv. Math.<\/em>, <strong>234<\/strong> (2013), 43-60.","DOI":"10.1016\/j.aim.2012.10.014"}],"container-title":["Advances in Mathematics of Communications"],"original-title":[],"link":[{"URL":"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=12520","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:05:32Z","timestamp":1772791532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2016006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016]]}},"URL":"https:\/\/doi.org\/10.3934\/amc.2016006","relation":{},"ISSN":["1930-5346","1930-5338"],"issn-type":[{"value":"1930-5346","type":"print"},{"value":"1930-5338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}