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On Unitals ith Many Baer Sublines

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Abstract

We identify the points of PG(2, q) ith the directions of lines in GF(q 3), viewed as a 3-dimensional affine space over GF(q). Within this frameork we associate to a unital in PG(2, q) a certain polynomial in to variables, and show that the combinatorial properties of the unital force certain restrictions on the coefficients of this polynomial. In particular, if q = p 2 where p is prime then e show that a unital is classical if and only if at least (q - 2)\(\sqrt q\) secant lines meet it in the points of a Baer subline.

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Authors and Affiliations

  1. Technische Universiteit Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    Simeon Ball & Aart Blokhuis

  2. Department of Pure Mathematics, The University of Adelaide, 5005, Australia

    Christine M. O'Keefe

Authors
  1. Simeon Ball
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  2. Aart Blokhuis
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  3. Christine M. O'Keefe
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Ball, S., Blokhuis, A. & O'Keefe, C.M. On Unitals ith Many Baer Sublines. Designs, Codes and Cryptography 17, 237–252 (1999). https://doi.org/10.1023/A:1026487412101

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  • DOI: https://doi.org/10.1023/A:1026487412101

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