Multiple ambient spaces for codes?

[David Lucas]

In some cases, it might be interesting to have an ambient space which is not a vector space (e.g. some people prefer to consider cyclic code's words as polynomials).

Is there an easy way to set that in our framework?

[Daniel Augot]

The other example is the case of codes in the rank metric, where the ambient space is the space of matrices. It makes no sense to flatten down matrices to make them codewords as vectors.

[Johan Rosenkilde]

I think this is an interesting possibility, but it requires extensive modification to how codes are implemented now! Basically, we should completely throw away the underlying F^n assumption in all that we have so far done, and rethink the entire basis of AbstractLinearCode.

I'm open to discussing this, but it's going to be a lot of work for a - possibly - quite academic gain.

I don't think rank metric codes should inherit from AbstractLinearCode. Two codewords are "the same codeword" if they represent the same vector space, and is in no way handled by the functionality you get from AbstractLinearCode. Therefore they might not be the best example.

[Daniel Augot]

I think you are mentioning "codes in the Grassmanian", where each codeword is a vector space.

But, there are various meanings for rank metric codes. I was thinking of codes like Gabidulin codes, and the ambient space is really the matrix space, and the codes are truly linear codes. In that setting, two matrices who generates the same vector space do not define the same codeword.

[Johan Rosenkilde]

Oh yes, you are right, I confused subspace codes with rank metric.