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The Jamison method in galois geometries

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Abstract

In a fundamental paper R.E. Jamison showed, among other things, that any subset of the points of AG(n, q) that intersects all hyperplanes contains at least n(q − 1) + 1 points. Here we show that the method of proof used by Jamison can be applied to several other basic problems in finite geometries of a varied nature. These problems include the celebrated flock theorem and also the characterization of the elements of GF(q) as a set of squares in GF(q 2) with certain properties. This last result, due to A. Blokhuis, settled a well-known conjecture due to J.H. van Lint and the late J. MacWilliams.

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Authors and Affiliations

  1. Department of Mathematics, Middlesex College, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    A. A. Bruen

  2. Department of Mathematics, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    J. C. Fisher

Authors
  1. A. A. Bruen
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  2. J. C. Fisher
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Communicated by S.A. Vanstone

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Bruen, A.A., Fisher, J.C. The Jamison method in galois geometries. Des Codes Crypt 1, 199–205 (1991). https://doi.org/10.1007/BF00123760

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