Geometry of the Mathieu groups and Golay codes
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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 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.
Volume 133, 2023
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