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 is isomorphic to the elementary abelian group of order 8
Borello, M., DALLA VOLTA, F., Nebe, G. (2013). The Automorphism Group of a Self-Dual [72; 36; 16] Code does not Contain S3, A4 OR D8. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 7(4), 503-510.
The Automorphism Group of a Self-Dual [72; 36; 16] Code does not Contain S3, A4 OR D8
BORELLO, MARTINO;DALLA VOLTA, FRANCESCA;
2013
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 is isomorphic to the elementary abelian group of order 8
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