Regular sets of lines in rank 3 polar spaces

2023/12/04 by Ferdinand Ihringer, Ihringer, Ferdinand, Morgan Rodgers +1
Computer Science · Mathematics · #05B25 #05E30 #51A50 #51E20 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2312.02397

openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There are 6 families of finite polar spaces of rank 3. The set of lines in a rank 3 polar space form a rank 5 association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some examples. We also give a new family of Cameron--Liebler sets of generators in the polar spaces O⁺(10,q) when q = 3^h using a regular set of lines in O(7,q).

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