Information set decoding for linear codes

[sagetrac-dlucas]

This ticket proposes an implementation of Lee-Brickell algorithm refinement for the information set decoding.

It depends on #19653 for the reimplementation of C.random_element.

Depends on #19653

CC: @jlavauzelle

Component: coding theory

Author: David Lucas, Johan Rosenkilde, Yann Laigle-Chapuy

Branch/Commit: eb2efb3

Reviewer: Yann Laigle-Chapuy

Issue created by migration from https://trac.sagemath.org/ticket/20138

[sagetrac-dlucas]

Branch: u/dlucas/information_set_decoding

[sagetrac-dlucas]

Commit: 645e329

[sagetrac-dlucas]

comment:2

I pushed the first version of the code for this ticket.

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New commits:

884d8ab	New decoder, InformationSetDecoder
351b30c	Set this new decoder in other code families and in the catalog
645e329	Fixed broken doctests

[sagetrac-git]

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

6292df9	window_size and number_errors are now class arguments
e72a5ab	Rewrote `_repr_` and `_latex_` methods, fixed a typo
f2c074c	decode_to_code now iterates over the whole range of provided errors
0e1391d	Added *args to Decoder/Encoder-related methods in AbstractLinearCode

[sagetrac-git]

Changed commit from 645e329 to 0e1391d

[sagetrac-dlucas]

Author: David Lucas

[sagetrac-dlucas]

comment:4

I made some changes:

• window_size and number_errors (previously p and w) are no longer parameters of decode_to_code but class arguments to provide at construction time. number_errors can be provided as a tuple/list, and in that case, the decoder will iterate over it when trying to decode a word.

• I completely reworked the documentation, explained how the algorithm works and added a lot of doctests.

• I completed input sanitization with some extra checks.

• I fixed a stupid bug: only **kwargs was considered on Decoder/Encoder-related methods from AbstractLinearCode, like decoder(). So, C.decoder('InformationSet', 2, 2) was not working...

This is now open for review.

[sagetrac-git]

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

8192769

Updated to 7.1beta6 and fixed conflicts

[sagetrac-git]

Changed commit from 0e1391d to 8192769

[sagetrac-git]

Changed commit from 8192769 to 924be79