The graphs of non-degenerate linear codes

We consider the Grassmann graph of k-dimensional subspaces an n-dimensional vector space over q-element field and its subgraph Γ(n,k)q which consists all non-degenerate linear [n,k]q codes. assume that 1<k<n−1. It is well-known every automorphism induced by a semilinear corresponding or isomorphism to dual second possibility realized only for n=2k. Our result following: if q≥3 k≠2, then can be uniquely extended graph; in case when q=k=2, there are subgraphs isomorphic such isomorphisms between these cannot automorphisms graph.