On unitals with many Baer sublines
type: Item
instance of: scholarly article
title: On unitals with many Baer sublines
zbMATH Open document ID: 0951.51004
DOI: 10.1023/A:1026487412101
author: Simeon Ball
author: Christine M. O'Keefe
author: Aart Blokhuis
published in: Designs, Codes and Cryptography
publication date: 2000-01-24T00:00:00Z
review text: After identifying points of \(\text{PG}(2,q)\) with the slopes of lines in \(\text{GF}(q^3)\), regarded as a \(3\)-dimensional affine space over the field \(\text{GF}(q)\), the authors associate to a unital \(\mathcal U\) in \(\text{PG}(2,q)\), a polynomial in two variables. They show that the combinatorial properties of \(\mathcal U\) yield some restrictions on the coefficients of the polynomial. Assuming \(q=p^2\), \(p\) a prime, they show that \(\mathcal U\) is classical if and only if it has at least \((q-2)\sqrt q\) Baer subplanes among its secants.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1392713
zbMATH Keywords: unital
zbMATH Keywords: Hermitian curve
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
full work available at URL: a:1026487412101
OpenAlex ID: W2147850789
description: scientific article; zbMATH DE number 1392713