{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T13:12:19Z","timestamp":1742994739636,"version":"3.40.3"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319106823"},{"type":"electronic","value":"9783319106830"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-10683-0_5","type":"book-chapter","created":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T15:54:11Z","timestamp":1427298851000},"page":"91-110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Non-extendable $$\\mathbb{F}_{q}$$ -Quadratic Perfect Nonlinear Maps"],"prefix":"10.1007","author":[{"given":"Ferruh","family":"\u00d6zbudak","sequence":"first","affiliation":[]},{"given":"Alexander","family":"Pott","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,11,10]]},"reference":[{"key":"5_CR1","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.jcta.2003.09.006","volume":"104","author":"S. Ball","year":"2003","unstructured":"S. Ball, The number of directions determined by a function over a finite field. J. Combin. Theory Ser. A 104, 341\u201335 (2003)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"1","key":"5_CR2","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.aim.2003.11.006","volume":"189","author":"S. Ball","year":"2004","unstructured":"S. Ball, M.R. Brown, The six semifield planes associated with a semifield flock. Adv. Math. 189(1), 68\u201387 (2004)","journal-title":"Adv. Math."},{"key":"5_CR3","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10623-009-9318-7","volume":"54","author":"J. Bierbrauer","year":"2010","unstructured":"J. Bierbrauer, New semifields, PN and APN functions. Des. Codes Cryptogr. 54, 189\u2013200 (2010)","journal-title":"PN and APN functions. Des. Codes Cryptogr."},{"key":"5_CR4","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/0097-3165(95)90100-0","volume":"70","author":"A. Blokhuis","year":"1995","unstructured":"A. Blokhuis, A.E. Brouwer, T. Szonyi, The number of directions determined by a function f on a finite field. J. Combin. Theory Ser. A 70, 349\u2013353 (1995)","journal-title":"J. Combin. Theory Ser. A"},{"key":"5_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12095-010-0022-2","volume":"3","author":"L. Budaghyan","year":"2011","unstructured":"L. Budaghyan, T. Helleseth, New commutative semifields defined by new PN multinomials. Cryptogr. Commun. 3, 1\u201316 (2011)","journal-title":"Cryptogr. Commun."},{"issue":"2","key":"5_CR6","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008344232130","volume":"15","author":"C. Carlet","year":"1998","unstructured":"C. Carlet, P. Charpin, V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptosystems. Des. Codes Cryptogr. 15(2), 125\u2013156 (1998)","journal-title":"Des. Codes Cryptogr."},{"key":"5_CR7","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/j.aim.2007.07.007","volume":"217","author":"R.S. Coulter","year":"2008","unstructured":"R.S. Coulter, M. Henderson, Commutative presemifields and semifields. Adv. Math. 217, 282\u2013304 (2008)","journal-title":"Adv. Math."},{"key":"5_CR8","doi-asserted-by":"crossref","unstructured":"R.S. Coulter, M. Henderson, On a conjecture on planar polynomials of the form XTr\n                n\n              (X) \u2212 uX. Finite Fields Appl. 21, 30\u201334 (2013)","DOI":"10.1016\/j.ffa.2013.01.003"},{"key":"5_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-62012-6","volume-title":"Finite Geometries","author":"P. Dembowski","year":"1968","unstructured":"P. Dembowski, Finite Geometries (Springer, Berlin, 1968)"},{"key":"5_CR10","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1090\/S0002-9947-1906-1500764-6","volume":"7","author":"L.E. Dickson","year":"1906","unstructured":"L.E. Dickson, On commutative linear algebras in which division is always uniquely possible. Trans. Am. Math. Soc. 7, 514\u2013522 (1906)","journal-title":"Trans. Am. Math. Soc."},{"key":"5_CR11","doi-asserted-by":"crossref","unstructured":"L.C. Grove, Classical Groups and Geometric Algebra. Graduate Studies in Mathematics, vol. 39 (AMS, Providence, 2002)","DOI":"10.1090\/gsm\/039"},{"key":"5_CR12","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.ffa.2009.05.001","volume":"15","author":"X.-D. Hou","year":"2009","unstructured":"X.-D. Hou, C. Sze, On certain diagonal equations over finite fields. Finite Fields Appl. 15, 633\u2013643 (2009)","journal-title":"Finite Fields Appl."},{"issue":"1","key":"5_CR13","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/S0021-8693(03)00411-3","volume":"270","author":"W.M. Kantor","year":"2003","unstructured":"W.M. Kantor, Commutative semifields and symplectic spreads. J. Algebra 270(1), 96\u2013114 (2003)","journal-title":"J. Algebra"},{"key":"5_CR14","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/0021-8693(65)90018-9","volume":"2","author":"D.E. Knuth","year":"1965","unstructured":"D.E. Knuth, Finite semifields and projective planes. J. Algebra 2, 153\u2013270 (1965)","journal-title":"J. Algebra"},{"key":"5_CR15","doi-asserted-by":"publisher","first-page":"1076","DOI":"10.1016\/j.ffa.2012.08.008","volume":"18","author":"M. Kyuregyan","year":"2012","unstructured":"M. Kyuregyan, F. \u00d6zbudak, Planarity of products of two linearized polynomials. Finite Fields Appl. 18, 1076\u20131088 (2012)","journal-title":"Finite Fields Appl."},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"M. Kyuregyan, F. \u00d6zbudak, A. Pott, Some planar maps and related function fields, in Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics, vol. 574, (American Mathematical Society, Providence, RI, 2012), pp.\u00a087\u2013114","DOI":"10.1090\/conm\/574\/11425"},{"key":"5_CR17","unstructured":"M. Lavrauw, O. Polverino, Finite semifields, in Current Research Topics in Galois Geometry, Chap. 6, ed. by J. De Beule, L. Storme (NOVA Academic Publishers, New York, 2011)"},{"key":"5_CR18","volume-title":"Finite Fields","author":"R. Lidl","year":"1997","unstructured":"R. Lidl, H. Niederrieter, Finite Fields (Cambridge University Press, Cambridge, 1997)"},{"key":"5_CR19","unstructured":"G. Marino, O. Polverino, R. Trombetti, On \n$$\\mathbb{F}_{q}$$\n-linear sets of PG(3,\u2009q\n              3) and semifields. J. Combin. Theory Ser. A 114, 769\u2013788 (2007)"},{"key":"5_CR20","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1016\/0021-8693(77)90231-9","volume":"47","author":"G. Menichetti","year":"1977","unstructured":"G. Menichetti, On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field. J. Algebra 47, 400\u2013410 (1977)","journal-title":"J. Algebra"},{"key":"5_CR21","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.ffa.2014.03.004","volume":"29","author":"F. \u00d6zbudak","year":"2014","unstructured":"F. \u00d6zbudak, A. Pott, Uniqueness of \n$$\\mathbb{F}_{q}$$\n-quadratic perfect nonlinear maps from \n$$\\mathbb{F}_{q^{3}}$$\n to \n$$\\mathbb{F}_{q}^{2}$$\n. Finite Fields Appl. 29, 49\u201388 (2014)","journal-title":"Finite Fields Appl."},{"key":"5_CR22","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.aim.2012.10.014","volume":"234","author":"A. Pott","year":"2013","unstructured":"A. Pott, Y. Zhou, A new family of semifields with 2 parameters. Adv. Math. 234, 43\u201360 (2013)","journal-title":"Adv. Math."},{"key":"5_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-4006-4","volume-title":"L\u00fcckenhafte Polynome \u00fcber endlichen K\u00f6rpern","author":"L. R\u00e9dei","year":"1970","unstructured":"L. R\u00e9dei, L\u00fcckenhafte Polynome \u00fcber endlichen K\u00f6rpern (Birkh\u00e4user, Basel, 1970)"},{"key":"5_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-76878-4","volume-title":"Algebraic Function Fields and Codes","author":"H. Stichtenoth","year":"2009","unstructured":"H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edn. (Springer, Berlin, 2009)","edition":"2"},{"key":"5_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ffa.2013.04.001","volume":"23","author":"M. Yang","year":"2013","unstructured":"M. Yang, S. Zhu, K. Feng, Planarity of mappings \n$$x\\mathrm{Tr}(x) - \\frac{\\alpha } {2}x$$\n on finite fields. Finite Fields Appl. 23, 1\u20137 (2013)","journal-title":"Finite Fields Appl."},{"key":"5_CR26","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.ffa.2008.09.002","volume":"15","author":"Z. Zha","year":"2009","unstructured":"Z. Zha, G. Kyureghyan, X. Wang, Perfect nonlinear binomials and their semifields. Finite Fields Appl. 15, 125\u2013133 (2009)","journal-title":"Finite Fields Appl."}],"container-title":["Open Problems in Mathematics and Computational Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-10683-0_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T23:21:43Z","timestamp":1676935303000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-10683-0_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319106823","9783319106830"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-10683-0_5","relation":{},"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"10 November 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}