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.

[arpitdm]

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.

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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.

[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.

David

[jsrn]

Replying to 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

[jsrn]

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

Best, Johan

[jsrn]

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

[git]

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

​64f446a	Merge branch 'develop' of git://trac.sagemath.org/sage into abstract_code
​53e445b	added base_ring and length parameter to AbstractCode
​5e6dffe	Fixed some dependencies. Category still set up wrong.
​ba4fc53	Merge branch 'abstract_code' into t/28073/abstract_code
​e8edfeb	Fixed unclean merge.
​880aebb	Fixed default decoder/encoder dependencies. Set to None by default.
​d115600	No category set up and base_field in AbstractCode. No encoder/decoder error msgs. Documentation and tests.
​82fdc3c	Merge branch 'develop' of git://trac.sagemath.org/sage into rank_metric
​5c0fd69	Merge branch 'develop' of git://trac.sagemath.org/sage into rank_metric
​a251c61	Inheriting from Abstract Code. Encoding, decoding methods. Generic LinearRankMetricCode class.

[git]

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

​05476b3

Generator matrix methods in AbstractLinearRankMetricCode

[git]

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

​524efc8	Inheriting from Abstract Code. Encoding, decoding methods. Generic LinearRankMetricCode class.
​77fc1e2	Generator matrix methods in AbstractLinearRankMetricCode
​08b6e4f	Merge branch 'u/gh-emes4/coding/linear_rank_metric' of git://trac.sagemath.org/sage into rank_metric