71 citations · 129 across the 18 of their papers we have counts for
21 papers
A unified framework for existing and new constructions of Neumaier graphs
Aida Abiad, Wouter Castryck, Maarten De Boeck +2
A Neumaier graph is a non-complete edge-regular graph containing a regular clique; it is called strictly Neumaier if it is not strongly regular. In this paper we present a construc…
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…
-Analogs of divisible design graphs and Deza graphs
Dean Crnkovic, Maarten De Boeck, Francesco Pavese +1
Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of -analogs of divisible design graphs and show tha…
Association schemes and orthogonality graphs on anisotropic points of polar spaces
Sam Adriaensen, Maarten De Boeck
In this paper, we study association schemes on the anisotropic points of classical polar spaces. Our main result concerns non-degenerate elliptic and hyperbolic quadrics in PG$(n,q…
Regular ovoids and Cameron-Liebler sets of generators in polar spaces
Maarten De Boeck, Jozefien D'haeseleer, Morgan Rodgers
Cameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this…
On the existence of small strictly Neumaier graphs
Aida Abiad, Maarten De Boeck, Sjanne Zeijlemaker
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In par…
Blocking subspaces with points and hyperplanes
Sam Adriaensen, Maarten De Boeck, Lins Denaux
In this paper, we characterise the smallest sets consisting of points and hyperplanes in , such that each -space is incident with at least one element of …
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…
-Analogs of strongly regular graphs
Michael Braun, Dean Crnković, Maarten De Boeck +2
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection…
On the sunflower bound for -spaces, pairwise intersecting in a point
Aart Blokhuis, Maarten De Boeck, Jozefien D'haeseleer
A -intersecting constant dimension subspace code is a set of -dimensional subspaces in a projective space PG(n,q), where distinct subspaces intersect in a -dimensional…
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…
Cameron-Liebler sets of generators in finite classical polar spaces
Maarten De Boeck, Morgan Rodgers, Leo Storme +1
Cameron-Liebler sets were originally defined as collections of lines (`line classes') in sharing certain properties with line classes of symmetric tactical decom…
A combinatorial characterisation of embedded polar spaces
Jan De Beule, Maarten De Boeck
Some classical polar spaces admit polar spaces of the same rank as embedded polar spaces (often arisen as the intersection of the polar space with a non-tangent hyperplane). In thi…
The Cameron-Liebler problem for sets
Maarten De Boeck, Leo Storme, Andrea Švob
Cameron-Liebler line classes and Cameron-Liebler k-classes in PG(2k+1,q) are currently receiving a lot of attention. Links with the Erdős-Ko-Rado results in finite projective space…
The second largest Erdős-Ko-Rado sets of generators of the hyperbolic quadrics
Maarten De Boeck
An Erdős-Ko-Rado set of generators of a hyperbolic quadric is a set of generators which are pairwise not disjoint. In this article we classify the second largest maximal Erdős-Ko-R…
The small Kakeya sets in , a conic
Maarten De Boeck
A Kakeya set in the linear representation , a non-singular conic, is the point set covered by a set of lines, one through each point of…
On the dual code of points and generators on the Hermitian variety
Maarten De Boeck, Peter Vandendriessche
We study the dual linear code of points and generators on a non-singular Hermitian variety . We improve the earlier results for , we solve the minimum d…
The largest Erdős-Ko-Rado sets in 2-(v,k,1) designs
Maarten De Boeck
An Erdős-Ko-Rado set in a block design is a set of pairwise intersecting blocks. In this article we study Erdős-Ko-Rado sets in 2-(v,k,1) designs, Steiner systems. The Steiner trip…
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…
Necessary conditions for the existence of 3-designs over finite fields with nontrivial automorphism groups
Maarten De Boeck, Anamari Nakic
A q-design with parameters t-(v,k,lambda_t)_q is a pair (V, B) of the v-dimensional vector space V over GF(q) and a collection B of k-dimensional subspaces of V, such that each t-d…
Entanglement-assisted quantum low-density parity-check codes
Yuichiro Fujiwara, David Clark, Peter Vandendriessche +2
This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit c…