S. Adriaensen

activity

20242026

collaborators

6 papers

math.CO2026

Skirting the $n$ -tuples

Sam Adriaensen, Ferdinand Ihringer, William J. Martin +1

Let $n \geq 2$ and $q \geq 2$ be given. The set $X = Z_{q}^{n}$ is a metric space of diameter $n$ under the Hamming metric $d (\cdot, \cdot)$ . We seek a smallest set $S \subseteq X$ t…

math.CO2026

Even Sets and Dual Projective Geometric Codes: A Tale of Cylinders

Sam Adriaensen

In this paper, we prove that the smallest even sets in $PG (n, q)$ , i.e. sets that intersect every line in an even number of points, are cylinders with a hyperoval as base. Thi…

math.CO2025

Intersection problems for linear codes and polynomials over finite fields

Sam Adriaensen

This paper proves a stability result for a variation of the Erdős-Ko-Rado theorem in the context of polynomials over finite fields. Let $F$ be a family of polynomials of d…

math.CO2025

A note on short minimal codes from subgeometries

Sam Adriaensen, Peter Sziklai, Zsuzsa Weiner

In a 2022, Bartoli, Cossidente, Marino, and Pavese proved that in the projective space $PG (3, q^{3})$ , one can find three $F_{q}$ -subgeometries such that the union of thei…

math.CO2024

Multisets with few special directions and small weight codewords in Desarguesian planes

Sam Adriaensen, Tamás Szőnyi, Zsuzsa Weiner

In this paper, we tie together two well studied topics related to finite Desarguesian affine and projective planes. The first topic concerns directions determined by a set, or even…

math.CO2024

Points below a parabola in affine planes of prime order

Sam Adriaensen, Zsuzsa Weiner

The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kis…