An Abstract Class for Rank Metric Codes

[arpitdm]

We propose to implement AbstractRankMetricCode, an abstract class for rank metric codes which will initialize the basic parameters that every rank metric code possesses. This will inherit from AbstractCode class. Further, we propose to add rank-metric based methods to compute distance, weight and allow for matrix to vector (and reverse) conversions between representations. Finally, we create a generic representative class LinearRankMetricCode as well as encoding (generator matrix, systematic) and decoding (nearest neighbour) methods.

CC: @sagetrac-dlucas @johanrosenkilde @dimpase @xcaruso @Adurand8 @mbombar @vbraun

Component: coding theory

Author: Arpit Merchant, Marketa Slukova, Johan Rosenkilde

Branch: 899d390

Reviewer: Dima Pasechnik, Johan Rosenkilde, Xavier Caruso

Issue created by migration from https://trac.sagemath.org/ticket/21226

[arpitdm]

Branch: u/arpitdm/abstract_linear_rank_metric_code_class

[arpitdm]

comment:2

1. I've written a basic constructor for the class along with a couple of getter methods.
2. I've added some modified rank-metric based methods.
3. And deleted some methods from the ALC class according to the schema described in past discussions. There's about 10 more that need to be deleted similarly. I'm trying to see if this be written more compactly. Open to ideas.

More to follow.

---

New commits:

7e4b3a3

added a very basic constructor, a couple of basic getter methods and deleted a couple of methods from ALC class. added some rank distance, rank weight, to_matrix_representation and from_matrix_representation.

[arpitdm]

Commit: 7e4b3a3

[sagetrac-dlucas]

comment:3

Hello,

I won't comment extensively for now, as there's still a lot to do.
I just have one small comment/remark to keep in mind for later: when you will work on documentation, remember to carefully explain which representation you chose (matrix vs. vector) and how to get the other one to be sure users do understand how this class works
and what they should expect from it.

David

[johanrosenkilde]

comment:4

Replying to @sagetrac-dlucas:

Hello,

I won't comment extensively for now, as there's still a lot to do.
I just have one small comment/remark to keep in mind for later: when you will work on documentation, remember to carefully explain which representation you chose (matrix vs. vector) and how to get the other one to be sure users do understand how this class works
and what they should expect from it.

Seconded. And remember to explain that this class only supports rank-metric codes which are linear over the big field!

Best,
Johan

[johanrosenkilde]

comment:5

What's the state of this? What is missing? When do you plan to do it?

Best,
Johan

[johanrosenkilde]

comment:6

I think the class should be call AbstractLinearRankMetricCode by the way. It's terribly long, but the Linear is important.

[emes4]

Changed commit from 7e4b3a3 to none

[emes4]

Dependencies: #28073

[emes4]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-We propose to implement `AbstractRankMetricCode`, an abstract class for rank metric codes which will initialize the basic parameters that every rank metric code possesses. This will inherit from `AbstractLinearCode` class so that all relevant methods can be accessed and the others will be deleted. Further, we propose to add rank-metric based methods to compute distance, weight and allow for matrix to vector (and reverse) conversions between representations.
+We propose to implement `AbstractRankMetricCode`, an abstract class for rank metric codes which will initialize the basic parameters that every rank metric code possesses. This will inherit from `AbstractCode` class. Further, we propose to add rank-metric based methods to compute distance, weight and allow for matrix to vector (and reverse) conversions between representations. Finally, we create a generic representative class `LinearRankMetricCode` as well as encoding (generator matrix, systematic) and decoding (nearest neighbour) methods.
 
 

[emes4]

Changed author from Arpit Merchant to Arpit Merchant, Marketa Slukova

[emes4]

Changed branch from u/arpitdm/abstract_linear_rank_metric_code_class to u/gh-emes4/coding/linear_rank_metric