#13771: Canonical Forms and Automorphism Groups of linear codes
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Reporter: tfeulner
| Owner: wdj
Type: enhancement
| Status: needs_review
Priority: major
| Milestone: sage-5.7
Component: coding theory
| Resolution:
Keywords: linear code, canonical form, automorphism group, semilinear
equivalent | Work issues:
Report Upstream: N/A
| Reviewers:
Authors: Thomas Feulner
| Merged in:
Dependencies: #13588, #13726, #13723, #13417
| Stopgaps:
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Changes (by tfeulner):
* status: new => needs_review
* dependencies: #6391, #13726, #13723, #13417 => #13588, #13726, #13723,
#13417
* milestone: sage-5.6 => sage-5.7
Old description:
> Two linear codes C, C' over a finite field F of length n are equivalent,
> if there is
>
> * a permutation pi in S,,n,,
> * a multiplication vector phi in F*^n^ (F* the unit group)
> * an automorphism alpha of F
>
> with C' = (phi, pi, alpha) C and the action is defined via
>
> (phi, pi, alpha) (c,,0,,, ..., c,,n-1,,) = ( alpha( c,,pi(0),,)
> phi,,0,,^-1^ , ... , alpha( c,,pi(n-1),,) phi,,n-1,,^-1^ )
>
> This patch adds an algorithm for calculating a unique representative
> within the equivalence class of a given linear code. Furthermore, it
> computes the automorphism group of the code as a byproduct.
>
> Finally, it can also deal with the action of subgroups of the
> semimonomial group.
>
> ----
> Apply:
>
> 1. #6391
>
> 2. #13726
>
> 3. #13723
>
> 4. #13417
>
> 5. [attachment:trac_13771-canonical_forms_linear_code.patch]
New description:
Two linear codes C, C' over a finite field F of length n are equivalent,
if there is
* a permutation pi in S,,n,,
* a multiplication vector phi in F*^n^ (F* the unit group)
* an automorphism alpha of F
with C' = (phi, pi, alpha) C and the action is defined via
(phi, pi, alpha) (c,,0,,, ..., c,,n-1,,) = ( alpha( c,,pi(0),,)
phi,,0,,^-1^ , ... , alpha( c,,pi(n-1),,) phi,,n-1,,^-1^ )
This patch adds an algorithm for calculating a unique representative
within the equivalence class of a given linear code. Furthermore, it
computes the automorphism group of the code as a byproduct.
Finally, it can also deal with the action of subgroups of the semimonomial
group.
----
Apply:
1. #13588
2. #13726
3. #13723
4. #13417
5. [attachment:trac_13771-canonical_forms_linear_code.patch]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13771#comment:4>
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