We associate binary codes to polynomials over fieldsof characteristic two and show that thebinary Golay codes are associated to the Mathieu group polynomialsin characteristic two. We give two more polynomials whose Galoisgroup is M_{12} but different ...
We associate binary codes to polynomials over fieldsof characteristic two and show that thebinary Golay codes are associated to the Mathieu group polynomialsin characteristic two. We give two more polynomials whose Galoisgroup is M_{12} but different self-orthogonal binary codes areassociated. Also, we find a family of M_{24}-coverings whichincludes previous ones.