Systematic encoder for linear codes

[sagetrac-dlucas]

This ticket introduces a generic systematic encoder for linear codes.

Depends on #20840

CC: @johanrosenkilde @ClementPernet

Component: coding theory

Author: David Lucas

Branch/Commit: 3a2f5ac

Reviewer: Johan Rosenkilde

Issue created by migration from https://trac.sagemath.org/ticket/20835

[sagetrac-dlucas]

Branch: u/dlucas/systematic_encoder

[sagetrac-dlucas]

comment:2

I pushed the code, this ticket is now open for review.

---

New commits:

54b50b7	Implemented a systematic encoder
ebe977b	Method generator_matrix_systematic now uses the encoder

[sagetrac-dlucas]

Author: David Lucas

[sagetrac-dlucas]

Commit: ebe977b

[sagetrac-git]

Changed commit from ebe977b to 7248f40

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

51205d0	Changed `_repr_` and `_latex_` output message. Replaced for the by for in such messages in other objects' representation methods
2d02053	Renamed rank_profile_colum_indices, simplified its implementation
7248f40	Rewrote class documentation of the encoder

[sagetrac-dlucas]

comment:4

I made some changes to this ticket:

• I simplified the output message of _repr_ and _latex_. I also noticed other encoders in linear_code.py were outputting Encoder blah for the Code blah, while Sage convention is to write Encoder blah for Code blah. I fixed this as well.

• I renamed rank_profile_column_indices into systematic_positions, and utterly simplified its implementation.

• I also added details on the encoding, and what we call "systematic form" to the class docstring.

This is still open for review.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

55f8771	Added automatic registration for generic encoder/decoders
550c584	Added a note to document this feature in related tutorial
ad1cadd	fixed broken doctest in the introductory tutorial
2887ee1	Merged trac #20840, fixed conflicts and broken doctets

[sagetrac-git]

Changed commit from 7248f40 to 2887ee1

[sagetrac-dlucas]

Dependencies: #20840

[sagetrac-dlucas]

comment:6

As this ticket introduces a new generic encoder, I merged in #20840 and made the appropriate changes.
It now depends on #20840 and is still open for review (and I'm done pushing changes now ;))

David

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5036711	Merge branch 'develop' into systematic_encoder
83cb47a	Systematic encoder now includes parity check encoder's behaviour. Deprecated parity check encoder
8dc72f5	Parity check encoder is no longer systematically imported. Reinstated it in hamming_code.py
46485e6	Removed useless imports
6d01e05	Fixed broken doctests
bb41e21	Merged latest version of #20835 and fixed conflicts

[sagetrac-git]

Changed commit from 2887ee1 to bb41e21

[sagetrac-dlucas]

comment:8

As LinearCodeParityCheckEncoder and LinearCodeSystematicEncoder were actually doing the same thing, I modified the latter so it now uses a parity check matrix when computing a generator matrix if it is the default encoder. I also deprecated the former.
I also merged in latest version of #20840 and fixed conflicts.

This is open for review.

David

[johanrosenkilde]

comment:9

In AbstractLinearCode.generator_matrix_systematic, shouldn't the method call AbstractLinearCode.encoder in order to use a possible cached systematic encoder?

Also, perhaps this ticket is as good a place as any to rename that method into systematic_generator_matrix and deprecate the old name.

Best,
Johan

[sagetrac-git]

Changed commit from bb41e21 to 2089792

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

170e79c	Merge branch 'u/dlucas/systematic_encoder' of git://trac.sagemath.org/sage into systematic_encoder
9ab771a	Renamed generator_matrix_systematic into systematic_generator_matrix, changed its implementation
2089792	Fixed broken doctest in subfield_subcode.py

[sagetrac-dlucas]

comment:11

Hello,

I made the requested changes.

David

[johanrosenkilde]

Changed branch from u/dlucas/systematic_encoder to u/jsrn/systematic_encoder

[johanrosenkilde]

Reviewer: Johan Rosenkilde

[johanrosenkilde]

comment:13

Good job with the patch. I made a few improvements to the doc. I also added a
check to avoid infinite recursion in case the user made a class with the systematic encoder as default encoder but forgot to override parity check matrix.

If you can accept my changes, please set the ticket to positive review.
Best,
Johan

---

New commits:

3e5e0b2	Improved some documentation
f90f4ee	Add a catch to avoid infinite loop in case of user error + examples
ab1cc5a	Fix to encoder catalog doc
3a2f5ac	Fixes to LinearCodeSystematicEncoder doc

[johanrosenkilde]

Changed commit from 2089792 to 3a2f5ac

[sagetrac-dlucas]

comment:14

Tests pass, documentation compiles and I accept your changes, I set this ticket to positive review.

David

[vbraun]

Changed branch from u/jsrn/systematic_encoder to 3a2f5ac