Add functionalities for GRS attack to linear_rank_metric.py

[MaaikevLeuken]

To perform the GRS attack described by Gaborit et al. in "On the complexity of the rank syndrome decoding problem", functionalities need to be added to AbstractLinearRankMetricCode to:

• Find an error vector of a certain rank.
• Apply the canonical projection to a element in the extended field.
• Find a subspace of the extended field of given dimension.
• Apply the GRS algorithm.

CC: @MaaikevLeuken

Component: coding theory

Keywords: rank code

Author: Maaike van Leuken

Branch/Commit: u/gh-MaaikevLeuken/add_low_rank_parity_check_codes @ a9a274e

Issue created by migration from https://trac.sagemath.org/ticket/31450

[mkoeppe]

comment:1

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[MaaikevLeuken]

New commits:

8c92768

Added Low Rank Parity Check codes and added functionalities for linear_rank_metric

[MaaikevLeuken]

Commit: 8c92768

[MaaikevLeuken]

Branch: u/gh-MaaikevLeuken/add_low_rank_parity_check_codes

[sagetrac-git]

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

a9a274e

Improved formatting.

[sagetrac-git]

Changed commit from 8c92768 to a9a274e