#13771: Canonical Forms and Automorphism Groups of linear codes
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Reporter: tfeulner | Owner: wdj
Type: enhancement | Status:
Priority: major | needs_review
Component: coding theory | Milestone: sage-5.13
Keywords: linear code, canonical form, | Resolution:
automorphism group, semilinear equivalent | Merged in:
Authors: Thomas Feulner | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #13726 | Stopgaps:
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Comment (by tfeulner):
Replying to [comment:12 vbraun]:
> Interface-wise, it would be nice to expose the different styles of
automorphism groups from linear code as
> {{{
> @cached_method
> def automorphism_group(self, morphisms="semilinear"):
> ...
> }}}
You are right, it would be nice to distinguish these different notions of
equivalence in
`automorhpism_group` and also in `canonical_representative`. I will change
that.
There is also the possibility to restrict the permutational part of the
action to Young subgroups.
This is non-standard, should I provide an interface for that, too?
> Then you wouldn't need `_canonize`.
My algorithm computes the canonical representative and the automorphism
group at the same time. Therefore I thought that I have to implement the
method `_canonize`, which guarantees that the computation is carried out
only once. But I think, I should define
{{{
@cached_method
def _canonize(self, equivalence="semilinear"):
...
}}}
instead and `automorphism_group` and `canonical_representative` need not
to be cached.
> and return the actual automorphism group, not a list of generators and
order. For that, you'd have to implement subgroups of the semimonomial
transformation groups as a parent ...
I agree, but I am not sure how difficult this task will become. I am not
working in academia anymore, so I am not sure if I will find enough time.
Maybe we could open a seperate ticket with someone else being responsible?
--
Ticket URL: <http://trac.sagemath.org/ticket/13771#comment:16>
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