# MATHIEU GROUP COVERINGS AND GOLAY CODES

• Yie, Ik-Kwon
• Published : 2002.03.01
• 88 7

#### 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 characteristics two. We give two more polynomials whose Galois group in $M_{12}$ 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

#### References

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