#13771: Canonical Forms and Automorphism Groups of linear codes
------------------------------------------------------------------------------------------+
       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:              
------------------------------------------------------------------------------------------+
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>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

-- 
You received this message because you are subscribed to the Google Groups 
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to 
[email protected].
For more options, visit this group at 
http://groups.google.com/group/sage-trac?hl=en.

Reply via email to