Annika Guenther (Aachen)

will speak on

The automorphism group of binary self-dual type II codes

Time: 4:00PM
Date: Mon 9th February 2009
Location: Mathematical Sciences Seminar Room [map]

Abstract: Self-dual binary codes are of particular interest in algebraic coding
theory, and have many practical applications. The best
error-correcting self-dual binary codes have the additional property
of being doubly-even (or Type II), which means that the weight of
every codeword, i.e. the number of its nonzero entries, is a multiple
of $4$.
In constructing these codes, it is often helpful to consider their
automorphism groups. For a binary code $C$ of length $n$, its
automorphism group is
$$
Aut(C):={ pi in Sym_n,;|; C pi =C},
$$
where $Sym_n$ is the symmetric group on $n$ points.
This talk presents a recent result, which says that the automorphism
group of a binary self-dual Type II code of length $n$ is always
contained in the alternating group $Alt_n$. Moreover, given a
subgroup $G le Sym_n$, sufficient conditions on $G$ will be given
such that $G$ is contained in the automorphism group of a binary
self-dual Type II code.

(This talk is part of the Algebra and Number Theory series.)

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