#13771: Canonical Forms and Automorphism Groups of linear codes
-------------------------------------------------+--------------------------
Reporter: tfeulner | Owner: wdj
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.6
Component: coding theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Thomas Feulner | Merged in:
Dependencies: #6391, #13726, #13723, #13417 | Stopgaps:
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Description changed by tfeulner:
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.
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. #6391
2. #13726
3. #13723
4. #13417
5. [attachment:trac_13771-canonical_forms_linear_code.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13771#comment:1>
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