2014/03/07 by Ilaria Cardinali, Cardinali, Ilaria, N. S. Narasimha Sastry +1
Computer Science · Engineering · Mathematics · #05C10 #51E12 #57M10 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05C10 #msc:51E12 #msc:57M10
paper · pdf · doi:10.48550/arxiv.1403.1714
arxiv created 2014/03/07 · openalex publication_date 2014/03/07 · arxiv updated 2014/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Q0 be the classical generalized quadrangle of order q = 2n arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry X having as points all the elliptic ovoids of Q0 and as lines the maximal pencils of elliptic ovoids of Q0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q ∖ Q0 where Q is the classical (q; q2)-generalized quadrangle admitting Q0 as a hyperplane. Then, we investigate the collinearity graph Γof X: In particular, we obtain a classification of the cliques of Γproving that they arise either from lines of Q or subgeometries of Q defined over F2