arXiv Open Access 2025

Regular fat linear sets

Valentino Smaldore Corrado Zanella Ferdinando Zullo

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Abstrak

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.

Topik & Kata Kunci

math.CO

Penulis (3)

Valentino Smaldore

Corrado Zanella

Ferdinando Zullo

Format Sitasi

APA MLA BibTeX

Smaldore, V., Zanella, C., Zullo, F. (2025). Regular fat linear sets. https://arxiv.org/abs/2511.04581

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓