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An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10}
Published 8 Sep 2011 in cs.IT and math.IT | (1109.1680v3)
Abstract: Let $C$ be an extremal self-dual binary code of length 72 and $g\in \Aut(C) $ be an automorphism of order 2. We show that $C$ is a free $\F_2<g>$ module and use this to exclude certain subgroups of order 8 of $\Aut (C)$. We also show that $\Aut(C)$ does not contain an element of order 10.
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