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Bulletin of the London Mathematical Society Advance Access originally published online on May 27, 2009
Bulletin of the London Mathematical Society 2009 41(5):769-778; doi:10.1112/blms/bdp026
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© 2009 London Mathematical Society

Automorphisms of doubly even self-dual binary codes

Annika Günther

Lehrstuhl D für Mathematik
RWTH Aachen University
52056 Aachen
Germany
annika.guenther@math.rwth-aachen.de

Gabriele Nebe

Lehrstuhl D für Mathematik
RWTH Aachen University
52056 Aachen
Germany

Received 21 October 2008. Revision received 18 December 2008.

The automorphism group of a binary doubly even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in FFormula, and G is contained in the alternating group.

2000 Mathematics Subject Classification 94B05 (primary), 20G25, 11E95 (secondary).


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