Consider the point line-geometry Pt(n, k) having as points all the [n, k]-linear codes having minimum dual distance at least t + 1 and where two points X and Y are collinear whenever X boolean AND Y is a [n, k -1]-linear code having minimum dual distance at least t + 1. We are interested in the collinearity graph Lambda t(n, k) of Pt(n, k). The graph Lambda t(n, k) is a subgraph of the Grassmann graph and also a subgraph of the graph Delta t(n, k) of the linear codes having minimum dual distance at least t +1 introduced in [9]. We shall study the structure of Lambda t(n, k) in relation to that of Delta t(n, k) and we will characterize the set of its isolated vertices. We will then focus on Lambda 1(n, k) and Lambda 2(n, k) providing necessary and sufficient conditions for them to be connected. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://
Cardinali, I., Giuzzi, L. (2024). Grassmannians of codes. FINITE FIELDS AND THEIR APPLICATIONS, 94 [10.1016/j.ffa.2023.102342].
Grassmannians of codes
Cardinali, Ilaria;
2024-01-01
Abstract
Consider the point line-geometry Pt(n, k) having as points all the [n, k]-linear codes having minimum dual distance at least t + 1 and where two points X and Y are collinear whenever X boolean AND Y is a [n, k -1]-linear code having minimum dual distance at least t + 1. We are interested in the collinearity graph Lambda t(n, k) of Pt(n, k). The graph Lambda t(n, k) is a subgraph of the Grassmann graph and also a subgraph of the graph Delta t(n, k) of the linear codes having minimum dual distance at least t +1 introduced in [9]. We shall study the structure of Lambda t(n, k) in relation to that of Delta t(n, k) and we will characterize the set of its isolated vertices. We will then focus on Lambda 1(n, k) and Lambda 2(n, k) providing necessary and sufficient conditions for them to be connected. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://File | Dimensione | Formato | |
---|---|---|---|
GrassmanniansCodes-rev.pdf
accesso aperto
Tipologia:
Pre-print
Licenza:
PUBBLICO - Pubblico con Copyright
Dimensione
339.85 kB
Formato
Adobe PDF
|
339.85 kB | Adobe PDF | Visualizza/Apri |
1-s2.0-S1071579723001843-main.pdf
accesso aperto
Tipologia:
PDF editoriale
Licenza:
Creative commons
Dimensione
423.05 kB
Formato
Adobe PDF
|
423.05 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/1256089