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arXiv · 1303.4899

The automorphism group of a self-dual [72,36,16] code does not contain S_3, A_4, or D_8

Martino Borello·Francesca Dalla Volta·Gabriele Nebe
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Abstract

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72, whose automorphism group contains the symmetric group of degree 3, the alternating group of degree 4 or the dihedral group of order 8. Combining this with the known results in the literature one obtains that Aut(C) has order at most 5 or isomorphic to the elementary abelian group of order 8.

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Martino Borello, Francesca Dalla Volta, Gabriele Nebe. 2013-03-20. The automorphism group of a self-dual [72,36,16] code does not contain S_3, A_4, or D_8. https://arxiv.org/abs/1303.4899

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