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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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 |
|---|---|
| Publication: | Proceedings of Indian Academy of Sciences- Mathematical Sciences |
| Publisher: | Indian Academy of Sciences |
| 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 (Ceased to exist at the end of 2003) Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 Sep 2008 09:20 |
| Last Modified: | 23 Sep 2008 09:20 |
| URI: | http://eprints.iisc.ac.in/id/eprint/15926 |
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