New decoders for Generalized Reed-Solomon codes

[sagetrac-dlucas]

This ticket introduces four new different decoders for GRS codes, namely:

• GRSBerlekampWelchDecoder,
• GRSGaoDecoder,
• GRSKeyEquationSyndromeDecoder and
• GRSErrorErasureDecoder.

It requires the new structure for GRS codes introduced in ticket #18928

Depends on #18928
Depends on #19897

CC: @johanrosenkilde

Component: coding theory

Author: David Lucas

Branch/Commit: f3b4b11

Reviewer: Julien Lavauzelle

Issue created by migration from https://trac.sagemath.org/ticket/19653

[sagetrac-dlucas]

Branch: u/dlucas/grs_decoders

[sagetrac-dlucas]

comment:2

I pushed the changes, it's now open for review.
Please note that I branched #18928 to work on this ticket.

---

New commits:

d854eb8	New Generalized Reed Solomon code object in Sage, coming with two encoders
0645f58	Updated to 6.9beta6 and fixed conflict
dc470be	Overwrote some methods from linear_code
f8c2d7a	Updated to 6.10beta0 and resolved conflicts
fa4dd71	Update to latest beta
1c1f182	Merged with latest beta version and fixed conflicts
74cc281	Four new decoders for GRS codes

[sagetrac-dlucas]

Author: David Lucas

[sagetrac-dlucas]

Commit: 74cc281

[sagetrac-git]

Changed commit from 74cc281 to b03d7b5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

8733405	Some improved doc-strings and doc-tests
229b5cf	Some code beautification
fe7e9de	Sanity-checks on input for GRSEvaluationPolynomialEncoder
6e7013b	Small doc-string improvements in linear_code and encoder
0e82848	More small docstring improvements
91e2e3b	Doc-string typesetting fix
eabe7e0	Reworked coercion of evaluation pts and col mults and refined tests.
71070de	Merged with 18928 and fixed conflicts
9f4fb84	Improved docstrings and doctests
b03d7b5	Extra cleaning in documentation

[sagetrac-dlucas]

comment:4

I merged in #18928 latest version and did some fixes and improvements to the documentation.

[sagetrac-git]

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

4e1a184

Merge branch 'develop' into grs_decoders

[sagetrac-git]

Changed commit from b03d7b5 to 4e1a184

[sagetrac-dlucas]

comment:6

Updated to latest beta, still open for review.