Simeon Ball

activity

20082026

most citedQuantum error-correcting codes and their geometries

10 citations · 23 across the 19 of their papers we have counts for

collaborators

Showing math.COShow all

13 papers · 1 filter

math.CO2026

Sets of subspaces with restricted hyperplane intersection numbers

Tim Alderson, Simeon Ball

Let $X$ be a set of $(h - 1)$ -dimensional subspaces of $PG (k h - 1, q)$ with the property that every hyperplane contains at most $t$ elements of $X$ . We prov…

math.CO2021

A polynomial time reduction from the multi-graph isomorphism problem to additive code equivalence

Simeon Ball, James Dixon

We present a polynomial time reduction from the multi-graph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of $F_{2}$ .

math.CO2019

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…

math.CO2019

Arcs and tensors

Simeon Ball, Michel Lavrauw

To an arc $A$ of $PG (k - 1, q)$ of size $q + k - 1 - t$ we associate a tensor in $⟨ ν_{k, t} (A) ⟩^{\otimes k - 1}$ , where $ν_{k, t}$ denotes the Veronese…

math.CO2019

On varieties defined by large sets of quadrics and their application to error-correcting codes

Simeon Ball, Valentina Pepe

Let $U$ be a $((2 k - 1) - 1)$ -dimensional subspace of quadratic forms defined on $PG (k - 1, F)$ with the property that $U$ does not contain any reducible quad…

math.CO2017★ 1 cited

On sets of points with few odd secants

Simeon Ball, Bence Csajbók

We prove that, for $q$ odd, a set of $q + 2$ points in the projective plane over the field with $q$ elements has at least $2 q - c$ odd secants, where $c$ is a constant and an odd secan…

math.CO2016★ 3 cited

On subsets of the normal rational curve

Simeon Ball, Jan De Beule

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 ar…

math.CO2016

Extending small arcs to large arcs

Simeon Ball

An arc is a set of vectors of the $k$ -dimensional vector space over the finite field with $q$ elements $F_{q}$ , in which every subset of size $k$ is a basis of the space, i…

math.CO2015

A finite version of the Kakeya problem

Simeon Ball, Aart Blokhuis, Diego Domenzain

Let $L$ be a set of lines of an affine space over a field and let $S$ be a set of points with the property that every line of $L$ is incident with at least $N$ points of $S$ . Let $…

math.CO2015

Forbidden subgraphs in the norm graph

Simeon Ball, Valentina Pepe

We show that the norm graph constructed in [J. Kollár, L. Rónyai and T. Szabó, Norm-graphs and bipartite Turán numbers, Combinatorica, 16 (1996) 399--406] with $n$ vertices about $…

math.CO2014

On the representability of the bi-uniform matroid

Simeon Ball, Carles Padró, Zsuzsa Weiner +1

Every bi-uniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of effi…

math.CO2012★ 1 cited

On sets of vectors of a finite vector space in which every subset of basis size is a basis II

Simeon Ball, Jan De Beule

This article contains a proof of the MDS conjecture for $k \leq 2 p - 2$ . That is, that if $S$ is a set of vectors of $F_{q}^{k}$ in which every subset of $S$ of size $k$ is a b…

math.CO2008

Symplectic spreads and permutation polynomials

Simeon Ball, Michael E. Zieve

Every symplectic spread of PG(3,q), or equivalently every ovoid of Q(4,q), is shown to give rise to a certain family of permutation polynomials of GF(q) and conversely. This leads…