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Sublines of Prime Order Contained in the Set of Internal Points of a Conic

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Abstract

In [2] it was shown that if q ≥ 4n2−8n+2 then there are no subplanes of order q contained in the set of internal points of a conic in PG(2,qn), q odd, n≥ 3. In this article we improve this bound in the case where q is prime to \(q > 2n^2-(4-2\sqrt{3})n+(3-2\sqrt{3})\), and prove a stronger theorem by considering sublines instead of subplanes. We also explain how one can apply this result to flocks of a quadratic cone in PG(3,qn), ovoids of Q(4,qn), rank two commutative semifields, and eggs in PG(4n−1,q).

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Authors and Affiliations

  1. Departament of Discrete Mathematics, Technische Universiteit Eindhoven, HG 9.55, PO Box 513, 5600, MB, The Netherlands

    Michel Lavrauw

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  1. Michel Lavrauw
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Correspondence to Michel Lavrauw.

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Communicated by: J.D. Key

AMS Classification:11T06, 05B25, 05E12, 51E15

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Lavrauw, M. Sublines of Prime Order Contained in the Set of Internal Points of a Conic. Des Codes Crypt 38, 113–123 (2006). https://doi.org/10.1007/s10623-004-5664-7

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  • DOI: https://doi.org/10.1007/s10623-004-5664-7

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