9 citations · 28 across the 35 of their papers we have counts for
36 papers · 1 filter
Nets of conics containing a double line in , even
Nour Alnajjarine, Michel Lavrauw
This paper completes the classification of nets of conics containing at least one double line in for even. This classification contributes to the classificat…
Linear complete symmetric rank-distance codes
Nour Alnajjarine, Michel Lavrauw
An -linear code of minimum distance is called complete if it is not contained in a larger -linear code of minimum distance . In this paper, we cl…
Webs and squabs of conics over finite fields
Nour Alnajjarine, Michel Lavrauw
This paper is a contribution towards a solution for the longstanding open problem of classifying linear systems of conics over finite fields initiated by L. E. Dickson in 1908, thr…
On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces
Michel Lavrauw, Stefano Lia, Francesco Pavese
The complete classification of the orbits on subspaces under the action of the projective stabiliser of (classical) algebraic varieties is a challenging task, and few classificatio…
A classification of planes intersecting the Veronese surface over finite fields of even order
Nour Alnajjarine, Michel Lavrauw
In this paper we contribute towards the classification of partially symmetric tensors in , even, by classifying planes which intersect…
Symplectic 4-dimensional semifields of order and
Michel Lavrauw, John Sheekey
We classify symplectic 4-dimensional semifields over , for , thereby extending (and confirming) the previously obtained classifications for . The cl…
On planar arcs of size
Gülizar Günay, Michel Lavrauw
The subject of this paper is the study of small complete arcs in , for odd, with at least points on a conic. We give a short comprehensive proof of…
Solids in the space of the Veronese surface in even characteristic
Nour Alnajjarine, Michel Lavrauw, Tomasz Popiel
We classify the orbits of solids in the projective space , even, under the setwise stabiliser of the Veronese surface. For each orbit,…
On pencils of cubics on the projective line over finite fields of characteristic
Gülizar Günay, Michel Lavrauw
In this paper we study combinatorial invariants of the equivalence classes of pencils of cubics on , for odd and not divisible by 3. These equivalence cla…
The Tensor Rank of Semifields of Order 16 and 81
Michel Lavrauw, John Sheekey
We determine the tensor rank of all semifields of order 16 over and of all semifields of order 81 over . Our results imply that some semifields of orde…
Combinatorial invariants for nets of conics in
Michel Lavrauw, Tomasz Popiel, John Sheekey
The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over …
Nets of conics of rank one in PG(2,q), q odd
Michel Lavrauw, Tomasz Popiel, John Sheekey
We classify nets of conics in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof…
Locally repairable codes with high availability based on generalised quadrangles
Michel Lavrauw, Geertrui Van de Voorde
Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in \cite{PaHoOg2013}, and bounds on the repairability and av…
Arcs in finite projective spaces
Simeon Ball, Michel Lavrauw
This is an expository article detailing results concerning large arcs in finite projective spaces, which attempts to cover the most relevant results on arcs, simplifying and unifyi…
Arcs and tensors
Simeon Ball, Michel Lavrauw
To an arc of of size we associate a tensor in , where denotes the Veronese…
The symmetric representation of lines in
Michel Lavrauw, Tomasz Popiel
Let be a finite field, an algebraically closed field, or the field of real numbers. Consider the vector space of mat…
Planar arcs
Simeon Ball, Michel Lavrauw
Let denote the characteristic of , the finite field with elements. We prove that if is odd then an arc of size in the projective plane over ${\ma…
Classification of 8-dimensional rank two commutative semifields
Michel Lavrauw, Morgan Rodgers
We classify the rank two commutative semifields which are 8-dimensional over their center . This is done using computational methods utilizing the connection to lin…
FinInG: a package for Finite Incidence Geometry
John Bamberg, Anton Betten, Philippe Cara +3
FinInG is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective s…
Scattered Spaces in Galois Geometry
Michel Lavrauw
This is a survey paper on the theory of scattered spaces in Galois geometry and its applications.
The BEL-rank of finite semifields
Michel Lavrauw, John Sheekey
In this article we introduce the notion of the BEL-rank of a finite semifield, prove that it is an invariant for the isotopism classes, and give geometric and algebraic interpretat…
Classification of subspaces in and orbits in
Michel Lavrauw, John Sheekey
This paper contains the classification of the orbits of elements of the tensor product spaces , , under the act…
Canonical forms of tensors over the real field, algebraically closed fields, and finite fields
Michel Lavrauw, John Sheekey
We classify the orbits of elements of the tensor product spaces for all finite; real; and algebraically closed fields…
Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs
Michel Lavrauw, Corrado Zanella
In this paper results are proved with applications to the orbits of -dimensional subspaces disjoint from a regulus $\cR$ of -subspaces in $\PG(2n-1,q)$, with respect…