The Jamison method in galois geometries

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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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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Keywords

  • Data Structure
  • Information Theory
  • Varied Nature
  • Basic Problem
  • Discrete Geometry