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    • Geometry of the Mathieu groups and Golay codes

      Eric A Lord

      Volume 98 Issue 2-3 December 1988 pp 153-177

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/098/02-03/0153-0177

    • 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

       
      Published
      December 1988
      Manuscript received
      11 January 1988

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