25 citations · 27 across the 23 of their papers we have counts for
25 papers
Pappus configurations in the Hall plane
Stefano Lia, John Sheekey, Geertrui Van de Voorde
In this paper, we investigate Pappus configurations in the finite affine Hall plane. In particular, we show that for any two lines and for any triple of points on $…
Anzahl theorems for trivially intersecting subspaces generating a non-singular subspace I: symplectic and hermitian forms
Maarten De Boeck, Geertrui Van de Voorde
In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace , we find the number o…
Triangle-free graphs with diameter 2
Alice Devillers, Nina Kamčev, Brendan McKay +5
There are finitely many graphs with diameter and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diamete…
Upper bounds for the number of substructures in finite geometries from the container method
Sam Mattheus, Geertrui Van de Voorde
We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this…
Characterising ovoidal cones by their intersection numbers
Bart De Bruyn, Geertrui Van de Voorde
In this paper, we characterise ovoidal cones by their intersection numbers. We first show that a set of points of which intersects planes in , or …
A note on strong blocking sets and higgledy-piggledy sets of lines
Stefano Lia, Geertrui Van de Voorde
This paper studies {\em strong blocking sets} in the -dimensional finite projective space . We first show that certain unions of blocking sets cannot form stro…
On Bruen chains
John Bamberg, Jesse Lansdown, Geertrui Van de Voorde
It is known that a Bruen chain of the three-dimensional projective space exists for every odd prime power at most , except for . It was shown by Ca…
A higgledy-piggledy set of planes based on the ABB-representation of linear sets
Lins Denaux, Jozefien D'haeseleer, Geertrui Van de Voorde
In this paper, we investigate the André/Bruck-Bose representation of certain -linear sets contained in a line of . We show that scattered $\mathbb{F…
Embedded antipodal planes and the minimum weight of the dual code of points and lines in projective planes of order
Maarten De Boeck, Geertrui Van de Voorde
The minimum weight of the code generated by the incidence matrix of points versus lines in a projective plane has been known for over 50 years. Surprisingly, finding the minimum we…
Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric \Q(2n,q)
Jeroen Schillewaert, Geertrui Van de Voorde
We provide a natural characterisation for the sets of elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q) when q is even. This characterisation is based on the num…
The weight distributions of linear sets in PG(1,q^5)
Maarten De Boeck, Geertrui Van de Voorde
In this paper, we study the weight distributions of -linear sets in . Our main theorem proves that a linear set of rank , which is not scat…
Exending pseudo-arcs in odd characteristic
Tim Penttila, Geertrui Van de Voorde
A {\em pseudo-arc} in is a set of -spaces such that any three of them span the whole space. A pseudo-arc of size is a {\em pseudo-oval}. If a p…
Constructing minimal blocking sets using field reduction
Geertrui Van de Voorde
We present a construction for minimal blocking sets with respect to -spaces in , the -dimensional projective space over the finite field $\mathb…
A linear set view on KM-arcs
Maarten De Boeck, Geertrui Van de Voorde
In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a differe…
Subgeometries in the André/Bruck-Bose representation
Sara Rottey, John Sheekey, Geertrui Van de Voorde
We consider the André/Bruck-Bose representation of the projective plane in . We investigate the representation of -subline…
Pseudo-ovals in even characteristic and ovoidal Laguerre planes
Sara Rottey, Geertrui Van de Voorde
Pseudo-arcs are the higher dimensional analogues of arcs in a projective plane: a pseudo-arc is a set of -spaces in such that any three s…
Linear representations of subgeometries
Stefaan De Winter, Sara Rottey, Geertrui Van de Voorde
The linear representation of a point set in a hyperplane of is a point-line geometry embedded in this projective space. In t…
Field reduction and linear sets in finite geometry
Michel Lavrauw, Geertrui Van de Voorde
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite ge…
On the linearity of higher-dimensional blocking sets
Geertrui Van de Voorde
A small minimal k-blocking set B in PG(n, q), q = pt, p prime, is a set of less than 3(qk + 1)/2 points in PG(n, q), such that every (n - k)-dimensional space contains at least one…
An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n, q)
Michel Lavrauw, Leo Storme, Peter Sziklai +1
Let Ck(n, q) be the p-ary linear code defined by the incidence matrix of points and k-spaces in PG(n, q), q = p^h, p prime, h >= 1. In this pa- per, we show that there are no codew…
A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime
Michel Lavrauw, Leo Storme, Geertrui Van de Voorde
In this paper, we show that a small minimal k-blocking set in PG(n, q3), q = p^h, h >= 1, p prime, p >=7, intersecting every (n-k)-space in 1 (mod q) points, is linear. As a coroll…
On codewords in the dual code of classical generalised quadrangles and classical polar spaces
Valentina Pepe, Leo Storme, Geertrui Van de Voorde
In [9], the codewords of small weight in the dual code of the code of points and lines of Q(4, q) are characterised. Inspired by this result, using geometrical arguments, we charac…
On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual
Michel Lavrauw, Leo Storme, Geertrui Van de Voorde
In this paper, we study the p-ary linear code Ck(n, q), q = ph, p prime, h >= 1, generated by the incidence matrix of points and k-dimensional spaces in PG(n, q). For k >= n/2, we…
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
Michel Lavrauw, Leo Storme, Geertrui Van de Voorde
In this paper, we study the p-ary linear code C(PG(n, q)), q = p^h, p prime, h >= 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space…