Regular fat linear sets
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915602732417024 |
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| author | Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando |
| author_facet | Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando |
| contents | In this work, we introduce $(r,i)$-regular fat linear sets, which are defined as linear sets containing exactly $r$ points of weight $i$ and all other points of weight one. This notion generalizes and unifies existing constructions; scattered linear sets, clubs, and other previously studied families are special cases. We present new classes of regular fat linear sets in PG$(k-1,q^n)$ for composite $n$ and study their equivalence classes. Finally, we show that regular fat linear sets naturally yield three-weight rank-metric codes, which we use to obtain bounds on their parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular fat linear sets Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando Combinatorics In this work, we introduce $(r,i)$-regular fat linear sets, which are defined as linear sets containing exactly $r$ points of weight $i$ and all other points of weight one. This notion generalizes and unifies existing constructions; scattered linear sets, clubs, and other previously studied families are special cases. We present new classes of regular fat linear sets in PG$(k-1,q^n)$ for composite $n$ and study their equivalence classes. Finally, we show that regular fat linear sets naturally yield three-weight rank-metric codes, which we use to obtain bounds on their parameters. |
| title | Regular fat linear sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.04581 |