On 3-designs from PGL(2,q)

2024/08/27 by Paul Tricot, Tricot, Paul
Computer Science · Engineering · #Antenna Design and Optimization #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.14714

openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The group PGL(2,q) acts 3-transitively on the projective line GF(q) ∪ \∞\. Thus, an orbit of its action on the k-subsets of the projective line is the block set of a 3-(q+1,k,λ) design. We find the parameters of the designs formed by the orbit of a block of the form ⟨ θ^r ⟩ or ⟨ θ^r ⟩ ∪ \ 0\, where θ is a primitive element of GF(q).

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