#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 darij):
Just saw this mentioned on sage-combinat-devel; sorry I can't be of any
actual help, so I thought I'll just drop a few remarks...
tfeulner: Given that you reference your thesis in the code, wouldn't it
make sense to put it online on, say, arXiv?
I don't understand what `_cyclic_shift` is supposed to do. What is being
cycled? If you want to get a cyclic permutation, why the `+ 1`'s in:
{{{
122 x[p[i - 1]] = p[i] + 1
123 x[p[len(p) - 1]] = p[0] + 1
}}}
"quadrupel" should be "quadruple".
{{{
45 For every `i \in \{0, \ldots, n-1\}`
46 there is a group `G^{(i)}` and a surjective group
homomorphism `f^{(i)}: G
47 \rightarrow G^{(i)}` such that `(f^{(i)}, \Pi^{(i)})`
is a homomorphism of
48 group actions where `\Pi^{(i)}: X^n \rightarrow X` is
the projection to
49 the `i`-th coordinate.
}}}
Isn't this a rather complicated way to say that the action of `G \rtimes
\{id\}` on `X^n` is given by a direct product of several `G`-sets `X` ? I
agree that the above is more precise, but can't you at least get rid of
the `G^{(i)}` by assuming it to be `G` right away?
--
Ticket URL: <http://trac.sagemath.org/ticket/13771#comment:19>
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