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Abstract

Galois fields and the finite Projective geometries that arise from them are introduced. The order of the collineation group for the finite geometry PG(N,q) is derived. Some particular cases with small values of N and q are described in detail. Some of the linear factional groups (homographies on finite projective lines) of special interest are presented and their relation to Steiner systems and Mathieu groups is explained. Finally, some remarkable special configurations are described, such as Coxeter’s ‘12 points in PG(5,3)’, and ‘24 points in PG(11,2)’, which are geometrical realizations of Golay’s ternary and binary codes.

Keywords

Projective Geometry Quadratic Residue Galois Field Steiner System Golay Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Eric Lord
    • 1
  1. 1.BangaloreIndia

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