[GAP Forum] Computing automorphism groups of codes over \F_9

[David Joyner]

Scott Anderson wrote:
> Hello to all,
>
> I am constructing codes over \F_9 and would like to
> compute the automorphism groups of these codes.  (I
> have the Guava package installed so as to be able to
> deal with codes in general.)  I seem to be running
> beyond some physical limitation of Gap, at least on
> my (sigh) Windows PC. 
>   

I'm not sure what you mean by "physical limitations". If you have
already tried using the -o option described in
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP003.htm#SECT001
then probably there is not much you can do with
whatever RAM you have.

> Is there some way to compute automorphism groups for
> such codes in a way that splits up the work (or
> something) so my computer doesn't gag on it?  Or
> would it be helpful to ask the larger Unix computer
> at the University to do this work?
>   

I don't know of a way to split up the work. The GAP code calling
the C code due to Leon is only implemented for binary codes. That
C code GAP calls should work for non-binary codes as well but
is not implemented in the non-binary case. (I tried to do this once
and never could get it to work properly.) Honestly, Leon's code needs
to be rewritten from scratch, but short of this you could try to
get GAP to call the C code in the non-binary case.
You would need to read Leon's documentation (which is very
sketchy), included with GUAVA in the src/leon/doc subdirectory.

> Any advice is appreciated.
>   

You can get an upper bound on the group by using
Thomas Breuer's MatrixAutomorphisms
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP069.htm#SECT020
Just put all the codewords of a given weight into a matrix
(each row is a codeword of weight 10 say) and apply the function.

Generally, the automorphism group computing ability of GUAVA is
poor. There are even known bugs in it
http://cadigweb.ew.usna.edu/%7Ewdj/gap/GUAVA/guava2do.html

> Cheers,
> Scott Anderson
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