Zero code, zero vector space and their Sage representation

As I was told to not bring this to any meeting (it might supposedly trigger never ending discussions), I'm posting this here.

I was playing with limit cases of Punctured Codes, and I tried to delete all the positions of the code. In that case, you got the zero code, whose base is empty: {Ø} and (as its a vector space) the set of its elements is reduced to 0.

I checked the Sage implementation: for a vector space of dimension 0, the base is empty, but also is the list of its elements:

sage: V = VectorSpace(GF(7), 0)
sage: V.basis()
[

]
sage: V.list()
[()]

(well, to be more specific, it contains only one elements, which is an empty vector).

Now, mathematically speaking, a vector space of dimension 0 must contain the zero vector, so the Sage implementation is not (imho) mathematically correct.

If we come back to codes, some interesting questions:

how to implement this? I could add some kind of check which returns 0 if one tries to get a vector of a zero code. Add a line like

if self.dimension() == 0:
    return self.ambient_space().zero()

to all methods like random_element and so on. Or maybe something more clever?

what about the distance? Such a code is MDS for sure, but is its distance n or n+1?
I settled the unencode question in #18376

So, what do you think about this?

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