Lins Denaux

activity

20192023

most citedConstructing saturating sets in projective spaces using subgeometries

11 citations · 28 across the 9 of their papers we have counts for

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9 papers · 1 filter

math.CO2023★ 2 cited

Small weight codewords of projective geometric codes II

Sam Adriaensen, Lins Denaux

The $p$ -ary linear code $C_{k} (n, q)$ is defined as the row space of the incidence matrix $A$ of $k$ -spaces and points of $PG (n, q)$ . It is known that if $q$ is squar…

math.CO2022

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 $F_{q}$ -linear sets contained in a line of $PG (2, q^{t})$ . We show that scattered $\mathbb{F…

math.CO2022

Blocking subspaces with points and hyperplanes

Sam Adriaensen, Maarten De Boeck, Lins Denaux

In this paper, we characterise the smallest sets $B$ consisting of points and hyperplanes in $PG (n, q)$ , such that each $k$ -space is incident with at least one element of $B$ …

math.CO2021

Two disguises of the linear representation of a subgeometry

Lins Denaux

Let $PG (n, q)$ be the Desarguesian projective space of dimension $n$ over the finite field of order $q$ . The \emph{linear representation} of a point set $K$ in a hy…

math.CO2021★ 5 cited

Higgledy-piggledy sets in projective spaces of small dimension

Lins Denaux

This work focuses on higgledy-piggledy sets of $k$ -subspaces in $PG (N, q)$ , i.e. sets of projective subspaces that are 'well-spread-out'. More precisely, the set of intersect…

math.CO2021★ 3 cited

Minimal codewords arising from the incidence of points and hyperplanes in projective spaces

Daniele Bartoli, Lins Denaux

Over the past few years, the codes $C_{n - 1} (n, q)$ arising from the incidence of points and hyperplanes in the projective space $PG (n, q)$ attracted a lot of attenti…

math.CO2020★ 11 cited

Constructing saturating sets in projective spaces using subgeometries

Lins Denaux

A $ϱ$ -saturating set of $PG (N, q)$ is a point set $S$ such that any point of $PG (N, q)$ lies in a subspace of dimension at most $ϱ$ spanned by poi…

math.CO2020★ 7 cited

Small Weight Code Words of Projective Geometric Codes

Sam Adriaensen, Lins Denaux

We investigate small weight code words of the $p$ -ary linear code $C_{j, k} (n, q)$ generated by the incidence matrix of $k$ -spaces and $j$ -spaces of PG $(n, q)$ and its dual,…

math.CO2019

Small weight code words arising from the incidence of points and hyperplanes in PG( $n, q$ )

Sam Adriaensen, Lins Denaux, Leo Storme +1

Let $C_{n - 1} (n, q)$ be the code arising from the incidence of points and hyperplanes in the Desarguesian projective space PG( $n, q$ ). Recently, Polverino and Zullo proved that within…

Small weight codewords of projective geometric codes II

A higgledy-piggledy set of planes based on the ABB-representation of linear sets

Blocking subspaces with points and hyperplanes

Two disguises of the linear representation of a subgeometry

Higgledy-piggledy sets in projective spaces of small dimension

Minimal codewords arising from the incidence of points and hyperplanes in projective spaces

Constructing saturating sets in projective spaces using subgeometries

Small Weight Code Words of Projective Geometric Codes

Small weight code words arising from the incidence of points and hyperplanes in PG(n,q)

Small weight code words arising from the incidence of points and hyperplanes in PG( $n, q$ )