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

Authors:
Anton Malevich;Wolfgang Willems
Affiliations:
Department of Mathematics, Otto-von-Guericke University Magdeburg, Magdeburg, Germany 39016;Department of Mathematics, Otto-von-Guericke University Magdeburg, Magdeburg, Germany 39016
Venue:
Designs, Codes and Cryptography
Year:
2014

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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.