Geometry of the Mathieu groups and Golay codes |
| |
Authors: | Eric A Lord |
| |
Institution: | 1. Centre for Theoretical Studies and Department of Applied Mathematics, Indian Institute of Science, 560 012, Bangalore, India
|
| |
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 ofM 24. 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 ofM 24. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|