Chow's theorem for linear codes

2016/03/19 by Mariusz Kwiatkowski, Kwiatkowski, Mariusz, Mark Pankov +1 · 1 citation
Mathematics · #51E22 #94B27 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:51E22 #msc:94B27

paper · pdf · doi:10.48550/arxiv.1603.06115

arxiv created 2016/03/19 · arxiv updated 2016/03/22

Abstract

Let Γ_k(V) be the Grassmann graph formed by k-dimensional subspaces of an n-dimensional vector space over the finite field \mathbb F_q consisting of q elements and 1<k<n-1. Denote by Γ(n,k)_q the restriction of the Grassmann graph to the set of all non-degenerate linear [n,k]_q codes. We describe maximal cliques of the graph Γ(n,k)_q and show that every automorphism of this graph is induced by a monomial semilinear automorphism of V.

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