Let $\Gamma(n,k)$ be the Grassmann graph formed by the $k$-dimensional subspaces of a vector space of dimension $n$ over a field $\mathbb F$ and, for $t\in \mathbb{N}\setminus \{0\}$, let $\Delta_t(n,k)$ be the subgraph of $\Gamma(n,k)$ formed by the set of linear $[n,k]$-codes having minimum dual distance at least $t+1$. We show that if $|{\mathbb F}|\geq{n\choose t}$ then $\Delta_t(n,k)$ is connected and it is isometrically embedded in $\Gamma(n,k)$. This generalizes some results of [M. Kwiatkowski, M. Pankov, "On the distance between linear codes", Finite Fields Appl. 39 (2016), 251--263] and [M. Kwiatkowski, M. Pankov, A. Pasini, "The graphs of projective codes" Finite Fields Appl. 54 (2018), 15--29].

翻译：Let\ gamma(n,k) $Grasmann 图形,由维度矢量空间的维度空间的维度子空间的维度子空间的 $1 美元形成, 美元= mathbb{N ⁇ setminus =0 $$, 美元= delta_ t(n,k) $= 伽马(n,k) $(n,k) 美元= 一组线性 $n,k) $(n,k) $(美元) 的子图。 我们显示,如果 美元=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx