id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
10153,Canonical generator matrices for linear codes and their automorphism groups,tfeulner,wdj,"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.",enhancement,closed,major,sage-duplicate/invalid/wontfix,coding theory,invalid,"Automorpism group, canonical representative",rlm burcin,,,Thomas Feulner,N/A,,,,,