#10153: Canonical generator matrices for linear codes and their automorphism
groups
------------------------------+---------------------------------------------
Reporter: tfeulner | Owner: wdj
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.6
Component: coding theory | Keywords: Automorpism group, canonical
representative
Author: Thomas Feulner | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Let R be a finite ring (up to now: a finite field or Z,,4,,). A submodule
of R^n^ is called a linear code of length n. Two linear codes C, C' over R
of length n are equivalent, if there is
* a permutation pi in S,,n,,
* a multiplication vector phi in R*^n^ (R* the set of invertible
elements)
* an automorphism alpha of R
with C' = (phi, pi, alpha) C and the action is defined via
(phi, pi, alpha) (c,,0,,, ..., c,,n-1,,) = ( phi,,0,, alpha(
c,,pi^-1^(0),,) , ... , phi,,n-1,, alpha( c,,pi^-1^(n-1),,) )
This patch adds an algorithm for calculating a unique representative
within the equivalence class of a given linear code (returning some unique
generator matrix). The algorithm calculates the automorphism group of the
code as a byproduct.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10153>
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