Publications

In this paper, we provide a construction of (q+1)-ovoids of the hyperbolic quadric Q+(7,q), q an odd prime power, by glueing (q+1)/2-ovoids of the elliptic quadric Q−(5,q). This is possible by controlling some intersection properties of (putative) m-ovoids of elliptic quadrics. It eventually yields (q+1)-ovoids of Q+(7,q) not coming from a 1-system. Secondly, for certain values of q, we construct line spreads of PG(3,q) that have as many ...

We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an Fq-linear (n,qhk,n−k+1)qh MDS code over Fqh. If k=3, h∈{2,3}, n>max⁡{qh−1,hq−1}+3, and C has three coordinates from which its projections are equivalent to Fqh-linear codes, we prove that C itself is equivalent to an Fqh-linear code. If k>3, n>q+k, and there are two disjoint subsets of ...

In this paper, we first determine the minimum possible size of an F q-linear set of rank k in PG(1,q n). We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q-linear set of rank k in PG(2,q n). In the case k=n, this confirms a conjecture by Sziklai in [9].

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 this article we look at sets of generators that behave combinatorially as the set of generators of such an embedded polar space, and we prove that they are the set of generators of an embedded polar space.

Combinatorial search problems in mathematics, e.g. in finite geometry, are notoriously hard; a state-of-the-art backtracking search algorithm can easily take months to solve a single problem. There is clearly demand for parallel combinatorial search algorithms scaling to hundreds of cores and beyond. However, backtracking combinatorial searches are challenging to parallelise due to their sensitivity to search order and due to the their ...

A normal rational curve of the (k -1)-dimensional projective space over F q is an arc of size q+1, since any k points of the curve span the whole space. In this paper, we will prove that if q is odd, then a subset of size 3k-6 of a normal rational curve cannot be extended to an arc of size q+2. In fact, we prove something slightly stronger. Suppose that q is odd and E is a (2k - 3)-subset of an arc G of size 3k - 6. If G projects to a subset ...