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

Martino Borello; Francesca Dalla Volta; Gabriele Nebe

doi:10.3934/amc.2013.7.503

Article Contents

2013, Volume 7, Issue 4: 503-510. Doi: 10.3934/amc.2013.7.503

This issue Previous Article Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbb{F}_{2^m}$ Next Article

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

1.
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, 20125 Milan
2.
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen

Received: March 2013

Revised: July 2013

Published: November 2013

Abstract / Introduction Related Papers Cited by

Abstract

A computer calculation with $M$AGMA shows that there is no extremal self-dual binary code $\mathcal{C}$ 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 $Aut(\mathcal{C})$ has order at most $5$ or is isomorphic to the elementary abelian group of order $8$.

Keywords:

Extremal self-dual code,
Automorphism group.

Mathematics Subject Classification: Primary: 94B05, 20B25.

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References

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