#13771: Canonical Forms and Automorphism Groups of linear codes
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Reporter: tfeulner | Owner: wdj
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.6
Component: coding theory | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Thomas Feulner
Merged in: | Dependencies: #6391, #13726, #13723, #13417
Stopgaps: |
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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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13771>
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