Yes. It is also a linear code.
A linear code of length n
and rank k
is a linear subspace C
with dimension k
of the vector space V.
Given subspaces U and W of a vector space V, then their intersection U ∩ W := {v ∈ V : v is an element of both U and W} is also a subspace of V.
To obtain H dimension this statement may be used:
Let (G,+G,∘)K be a K-vector space. Let M and N be finite-dimensional subspaces of G.
Then M+N and M∩N are finite-dimensional, and:
dim(M+N) + dim(M∩N) = dim(M) + dim(N)
so:
dim(M+N) + dim(M∩N) = k1 + k2
where dim(M∩N) is new k of the intersection.