The known maximal partial ovoids of size q²-1 of Q(4,q)

2012/01/28 by Kris Coolsaet, Coolsaet, Kris, Jan De Beule +3
Computer Science · Engineering · Mathematics · #05B25 #51D20 #51E12 #51E20 #51E21 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B25 #msc:51D20 #msc:51E12 #msc:51E20 #msc:51E21

paper · pdf · doi:10.48550/arxiv.1201.5967

15 pages, revised version (v2 on arxiv is just a update of another paper, applied on this paper, clearly a mistake...)

openalex publication_date 2012/01/28 · arxiv created 2012/02/01 · arxiv updated 2012/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a description of maximal partial ovoids of size q²-1 of the parabolic quadric \q(4,q) as sharply transitive subsets of \SL(2,q) and show their connection with spread sets. This representation leads to an elegant explicit description of all known examples. We also give an alternative representation of these examples which is related to root systems.

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