The automorphism group of binary self-dual type II codes

Speaker: Annika Guenther (Aachen)

Time: 4:00PM

Date: Mon 9th February 2009

Location: Mathematical Sciences Seminar Room

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/Claude Shannon Institute series.)