Support codes in rank metric

[David Lucas]

This weekend, I had the opportunity to discuss with a couple of PhD students who are working on codes and cryptography.

So, I tried to do a bit of advertisement for Sage and ACTIS, and it appears these students were working with codes in rank metric.

As this situation already happened to me several times when I discussed with PhD students, I somehow feel rank metric is a hot topic these days (if I can say it this way).

So, my question is:

Do you think it could be a good idea to (at some point) spend some time to support codes in rank metric?

Note that I do not really have an idea of the amount of work needed here. It will probably require to rethink a lot of things, because the actual structure is not made to manage something else than Hamming metric, but I really think it could help a lot of people.

Note also that I do think that it should be done (if done) after benchmarking and performance diagram, which makes this discussion highly hypothetical...

[Daniel Augot]

From the implementation side, it is not that much a big deal to have the rank metric and Gabidulin codes. You can implement a basic Berlekamp Welch, but this requires skew-polynomial rings.

Before going into this, it must be investigated a) if skew-polynomial ring are here, and b) if dealing the rank metric does not imply too much refactoring of the framework.

I can quickly lecture you on these codes, if needed.

Daniel

[David Lucas]

Ok, to clarify things a bit:

• I'm 100% sure we discussed this before, at least Johan and I did. I thought an issue has been opened about it, but it seems not, so I opened this one as a remainder on this topic.

• If I remember correctly, we found some things in the actual framework which are made for Hamming metric and only Hamming metric... Which implies expanding the framework to support other metrics won't be an easy process. I cannot remember a specific example though.

• I was definitely not considering the implementation of something advanced. If I do such a thing, it'll probably be around end of June (if all goes smoothly before) and I was just proposing to implement a framework to support such a metric, and let interested users do their own code.

[David Lucas]

Submitted to GSoC '16