On the weight distribution of linear sets with complementary weights and related constructions

2025/11/25 by Van de Voorde, Geertrui, Zullo, Ferdinando
Computer Science · Mathematics · Engineering · #Graph Labeling and Dimension Problems #Mathematical Analysis and Transform Methods #PAPR reduction in OFDM

paper · doi:10.48550/arxiv.2511.20057

Abstract

In this paper, we continue the study of linear sets with complementary weights. We find criteria to determine the set of points of any fixed weight and use this to present particular linear sets with few points of weight more than one. We also present a product-type construction for linear sets of complementary type arising from any linear set, allowing us to control the weight distribution of the obtained linear set. Finally, we use this construction to create linear sets with many different weights, along with point sets of even type with many distinct intersection numbers.

Citations

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Related

• Linear sets on the projective line with complementary weights
• The weight distributions of linear sets in PG(1,q⁵)
• Classifications and constructions of minimum size linear sets
• On linear sets of minimum size
• Regular fat linear sets