On the Grassmann graph of linear codes
| Autor: | Ilaria Cardinali, Mariusz Kwiatkowski, Luca Giuzzi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Projective codes
FOS: Computer and information sciences Grassmannians Collinearity Graphs Discrete Mathematics (cs.DM) Dimension (graph theory) Field (mathematics) Theoretical Computer Science Combinatorics Linear codes Diameter FOS: Mathematics Mathematics - Combinatorics Mathematics Algebra and Number Theory Applied Mathematics General Engineering Grassmann graph Linear subspace 51E22 94B27 Graph (abstract data type) Combinatorics (math.CO) Computer Science - Discrete Mathematics Vector space |
| Zdroj: | Finite Fields and Their Applications. 75:101895 |
| ISSN: | 1071-5797 |
| Popis: | 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]. Comment: 13 pages/final version |
| Databáze: | OpenAIRE |
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