The automorphism group of an extremal [72,36,16] code does not contain Z₇, Z₃ x Z₃, or D₁₀

Titelangaben

Feulner, Thomas ; Nebe, Gabriele:
The automorphism group of an extremal [72,36,16] code does not contain Z₇, Z₃ x Z₃, or D₁₀.
In: IEEE Transactions on Information Theory. Bd. 58 (2012) Heft 11 . - S. 6916-6924.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2012.2208176

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Abstract

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72 that has an automorphism group containing either the dihedral group of order 10, the elementary abelian group of order 9, or the cyclic group of order 7. Combining this with the known results in the literature, one obtains that the order of Aut(C) is either 5 or divides 24.