New hemisystems of the Hermitian surface

2021/05/20 by Vincenzo Pallozzi Lavorante, Valentino Smaldore, Lavorante, Vincenzo Pallozzi +1
Computer Science · Mathematics · #05B25 #05E30 #51E20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2105.09656

openalex publication_date 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of Hemisystems in PG(3,p²), for each prime of the form p=1+4a², with a integer. Last, we use these results to obtain two weight linear codes and strongly regular graphs.

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