Regular fat linear sets
Valentino Smaldore, Corrado Zanella, Ferdinando Zullo

TL;DR
This paper introduces a new class of linear sets called regular fat linear sets, unifying previous concepts, and explores their properties, equivalence classes, and applications to three-weight rank-metric codes.
Contribution
It defines regular fat linear sets, generalizes existing constructions, and links them to rank-metric codes with new bounds.
Findings
New classes of regular fat linear sets in projective spaces for composite n
Characterization of equivalence classes of these sets
Connection to three-weight rank-metric codes and parameter bounds
Abstract
In this work, we introduce -regular fat linear sets, which are defined as linear sets containing exactly points of weight 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 for composite 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.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research
