12-05
On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups
Preprint series: 12-05, Preprints
- MSC:
- 94B05 Linear codes, general
- 20B20 Multiply transitive finite groups
- 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures, See also {05Bxx, 12F10, 20G40, 20H30, 51-XX}
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
Upload:2012-03-13-03-13