On the classification of semifield flocks |
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Authors: | Aart Blokhuis Simeon Ball |
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Institution: | a Technische Universiteit Eindhoven, Postbox 513, 5600 MB Eindhoven, The Netherlands b Queen Mary, University of London, London E1 4NS, UK |
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Abstract: | A classical lemma of Weil is used to characterise quadratic polynomials f with coefficients GF(qn), q odd, with the property that f(x) is a non-zero square for all x∈GF(q). This characterisation is used to prove the main theorem which states that there are no subplanes of order q contained in the set of internal points of a conic in PG(2,qn) for q?4n2−8n+2. As a corollary to this theorem it then follows that the only semifield flocks of the quadratic cone of PG(3,qn) for those q exceeding this bound are the linear flocks and the Kantor-Knuth semifield flocks. |
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Keywords: | 51E99 12K10 |
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