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Geometry of the Mathieu groups and Golay codes

Lord, Eric A (1988) Geometry of the Mathieu groups and Golay codes. In: Proceedings of Indian Academy of Sciences- Mathematical Sciences, 98 (2-3). pp. 153-177.

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Official URL: http://www.springerlink.com/content/n16v5576005788...

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 in PG(5,3) and Todd’s configuration in PG(11,2) when interpreted projectively. We obtain two twelve-dimensional representations of$M_{24}$. One is obtained as the collineation group that permutes the twelve special points in PG(11,2); the other arises by interpreting geometrically the automorphism group of the binary Golay code. Both representations are reducible to eleven-dimensional representations of$M_{24}$.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Springer.
Keywords: Geometry;Mathieu groups;Golay codes;Coxeters configuration;hemi-icosahedron;octastigms;dodecastigms
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 23 Sep 2008 09:20
Last Modified: 23 Sep 2008 09:20
URI: http://eprints.iisc.ernet.in/id/eprint/15926

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