The edge code of hypergraphs
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911825804656640 |
|---|---|
| author | Jaramillo-Velez, Delio |
| author_facet | Jaramillo-Velez, Delio |
| contents | Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the minimum distance, particularly in scenarios involving $d$-uniform clutters. Additionally, we demonstrate that these codes exhibit self-orthogonality. Furthermore, we compute the minimum distances of edge codes for all graphs with five vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The edge code of hypergraphs Jaramillo-Velez, Delio Commutative Algebra Information Theory Combinatorics Primary 13P25, Secondary 05C65, 14G50, 94B27 Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the minimum distance, particularly in scenarios involving $d$-uniform clutters. Additionally, we demonstrate that these codes exhibit self-orthogonality. Furthermore, we compute the minimum distances of edge codes for all graphs with five vertices. |
| title | The edge code of hypergraphs |
| topic | Commutative Algebra Information Theory Combinatorics Primary 13P25, Secondary 05C65, 14G50, 94B27 |
| url | https://arxiv.org/abs/2404.02301 |