Improvements to systematic encoder for linear codes

[johanrosenkilde]

#20835 introduced a systematic encoder for linear codes which always obtains as the systematic positions the lexicographically minimal possibility. It would be nice if the user could specify the systematic positions.

At the same time, one could improve some methods of AbstractLinearCode to take advantage of the new improved systematic capabilities.

Depends on #20835

CC: @sagetrac-dlucas

Component: coding theory

Keywords: linear code

Author: Johan Rosenkilde

Branch/Commit: e46b9ff

Reviewer: David Lucas

Issue created by migration from https://trac.sagemath.org/ticket/21157

[johanrosenkilde]

Branch: u/jsrn/21157_improved_systematic

[johanrosenkilde]

comment:2

I've implemented the systematic encoder improvements as well as employed the new capabilities to simplify a few methods in AbstractLinearCode.

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Last 10 new commits:

3a2f5ac	Fixes to LinearCodeSystematicEncoder doc
a8a37bd	Implement optional systematic positions + examples
084fcc4	Fixed bug. Added example/test for non-information set systematic_positions
11a0e31	Shortcut with AbstractLinearCode.systematic_generator_matrix
e26a379	information_set can use systematic encoder
9e80364	Added is_information_set
4d56371	Simplified permuted_code (noticed in passing, nothing to do with systematic)
bc6b129	Simplified redundancy_matrix and improved its documentation
6882f91	Massively simplified AbstractLinearCode.standard_form and improved its doc
e46b9ff	Small doc improvements

[johanrosenkilde]

Changed keywords from linear cod to linear code

[johanrosenkilde]

Commit: e46b9ff

[sagetrac-dlucas]

comment:3

Hello,

Tests pass and documentation builds, and you made nice improvements (included a few I was about to open a ticket for, like the improvement to redundancy_matrix's doc :)).

I give this ticket a positive review.

David

[sagetrac-dlucas]

Dependencies: #20835

[vbraun]

comment:4

Reviewer name is missing

[sagetrac-dlucas]

Reviewer: David Lucas

[sagetrac-dlucas]

comment:5

Sorry...

Done now.

David

[vbraun]

Changed branch from u/jsrn/21157_improved_systematic to e46b9ff