Let Γ(n, k) be the Grassmann graph formed by the k- dimensional subspaces of a vector space of dimension n over a field F and, for t ∈ N {0}, let Δ t (n, k) be the subgraph of Γ(n, k) formed by the set of linear [n, k]-codes having minimum dual distance at least t +1. We show that if |F| ≥ nt then Δ t (n, k) is connected and it is isometrically embedded in Γ(n, k).
On the Grassmann graph of linear codes
Giuzzi, Luca;
2021-01-01
Abstract
Let Γ(n, k) be the Grassmann graph formed by the k- dimensional subspaces of a vector space of dimension n over a field F and, for t ∈ N {0}, let Δ t (n, k) be the subgraph of Γ(n, k) formed by the set of linear [n, k]-codes having minimum dual distance at least t +1. We show that if |F| ≥ nt then Δ t (n, k) is connected and it is isometrically embedded in Γ(n, k).File in questo prodotto:
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