Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2002; 39(2): 289-317

Printed March 1, 2002

Copyright © The Korean Mathematical Society.

Mathieu group coverings and Golay codes

Ikkwon Yie

Inha University

Abstract

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