• Geometry of the Mathieu groups and Golay codes

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    • Keywords


      Geometry; Mathieu groups; Golay codes; Coxeter’s configuration; hemi-icosahedron; octastigms; dodecastigms

    • Abstract


      A brief review is given of the linear fractional subgroups of the Mathieu groups. The main part of the paper then deals with the projective interpretation of the Golay codes; these codes are shown to describe Coxeter’s configuration inPG(5,3) and Todd’s configuration inPG(11,2) when interpreted projectively. We obtain two twelve-dimensional representations ofM24. One is obtained as the collineation group that permutes the twelve special points inPG(11,2); the other arises by interpreting geometrically the automorphism group of the binary Golay code. Both representations are reducible to eleven-dimensional representations ofM24.

    • Author Affiliations


      Eric A Lord1

      1. Centre for Theoretical Studies and Department of Applied Mathematics, Indian Institute of Science, Bangalore - 560 012, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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