Regular fat linear sets
Abstract
Abstract 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 $${{\,\textrm{PG}\,}}(k-1,q^n)$$ 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.
Fields of Study & Subjects
Coding theory and cryptography
graph theory and CDMA systems
Finite Group Theory Research
Publication details
- Journal / source
- Designs Codes and Cryptography
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 9
- Publication date
- 1 September 2026
- Language
- EN