Abstract
Let V be an n-dimensional vector space over the finite field consisting of q elements and let Γk(V) be the Grassmann graph formed by k-dimensional subspaces of V, 1<k<n−1. Denote by Γ(n,k)q the restriction of Γk(V) to the set of all non-degenerate linear [n,k]q codes. We show that for any two codes the distance in Γ(n,k)q coincides with the distance in Γk(V) only in the case when n<(q+1)2+k−2, i.e. if n is sufficiently large then for some pairs of codes the distances in the graphs Γk(V) and Γ(n,k)q are distinct. We describe one class of such pairs.
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