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2012-05

On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

by Malevich, A., Willems, W..


Series: 2012-05, Preprints

MSC:
94B05 Linear codes, general
20B20 Multiply transitive finite groups
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures

Abstract:
There are seven binary extremal self-dual doubly-even codes which are known to have a $2$-transitive automorphism group.
Using representation theoretical methods we show that there are no other such codes, except possibly for length $n = 1024$. We also classify all extremal ternary self-dual and quaternary Hermitian self-dual codes.

Keywords:
Automorphisms, Self-dual codes, Transitive groups, Simple groups