J. Korean Math. Soc. 2002; 39(2): 289-317
Printed March 1, 2002
Copyright © The Korean Mathematical Society.
Ikkwon Yie
Inha University
We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristic two. We give two more polynomials whose Galois group is $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.
Keywords: unramified coverings, Galois group, Mathieu group, Golay code
MSC numbers: 12F10
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