An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10}

Details An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10} An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10}

2011-09-08

arxiv.org/abs/1109.1680v3

Computer Science

Information Theory

This is the final version to appear in Finite fields and their applications

Scientific paper

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 $\F_2$ 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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