  Motivated by applications to noncoherent network coding, we study subspace
codes defined by sets of linear cellular automata (CA). As a first remark, we
show that a family of linear CA where the local rules have the same diameter --
and thus the associated polynomials have the same degree -- induces a
Grassmannian code. Then, we prove that the minimum distance of such a code is
determined by the maximum degree occurring among the pairwise greatest common
divisors (GCD) of the polynomials in the family. Finally, we consider the
setting where all such polynomials have the same GCD, and determine the
cardinality of the corresponding Grassmannian code. As a particular case, we
show that if all polynomials in the family are pairwise coprime, the resulting
Grassmannian code has the highest minimum distance possible.
