Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909964021268480 |
|---|---|
| author | Abiad, Aida Reijnders, Harper Tait, Michael |
| author_facet | Abiad, Aida Reijnders, Harper Tait, Michael |
| contents | We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that asymptotically $\mathbb{F}_q^{\mathbf{n} \times \mathbf{m}}$ can be partitioned into sum-rank-metric codes whose average size is bigger than the GV bound by a logarithmic factor for these parameters. Finally, we discuss the connection of such codes to set-coloring Ramsey numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory Abiad, Aida Reijnders, Harper Tait, Michael Combinatorics We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that asymptotically $\mathbb{F}_q^{\mathbf{n} \times \mathbf{m}}$ can be partitioned into sum-rank-metric codes whose average size is bigger than the GV bound by a logarithmic factor for these parameters. Finally, we discuss the connection of such codes to set-coloring Ramsey numbers. |
| title | Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.21298 |