Browsing by Author "Ball, Simeon Michael"
Now showing items 120 of 27

A bound for the maximum weight of a linear code
Ball, Simeon Michael; Blokhuis, Aart (20130321)
Article
Open AccessIt is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m ... 
A finite version of the Kakeya problem
Ball, Simeon Michael; Blokhuis, Aart; Domenzain, Diego (20160602)
Article
Open AccessLet 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 D be the set of directions of the lines of L considered ... 
A generalisation of Sylvester's problem to higher dimensions
Ball, Simeon Michael; Monserrat, Joaquim (20170701)
Article
Open AccessIn this article we consider $S$ to be a set of points in $d$space with the property that any $d$ points of $S$ span a hyperplane and not all the points of $S$ are contained in a hyperplane. The aim of this article is to ... 
ALA: Examen FQ: Primavera
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 20190603)
Exam
Restricted access to the UPC academic community 
ALA: Examen FQ: Tardor
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 20190110)
Exam
Restricted access to the UPC academic community 
ALA: Examen MQ: Primavera
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 20190325)
Exam
Restricted access to the UPC academic community 
ALA: Examen MQ: Tardor
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 20191029)
Exam
Restricted access to the UPC academic community 
Arcs and tensors
Ball, Simeon Michael; Lavrauw, Michel (20190801)
Article
Open AccessTo an arc A of PG(k1,q) of size q+k1t we associate a tensor in ¿¿k,t(A)¿¿k1 , where ¿k,t denotes the Veronese map of degree t defined on PG(k1,q) . As a corollary we prove that for each arc A in PG(k1,q) of size ... 
Arcs in finite projective spaces
Ball, Simeon Michael; Lavrauw, Michel (20191123)
Article
Restricted access  publisher's policyThis is an expository article detailing results concerning large arcs in finite projective spaces. It is not strictly a survey but attempts to cover the most relevant results on arcs, simplifying and unifying proofs of ... 
COMBINATÒRIA I TEORIA DE GRAFTS  Final
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 202001)
Exam
Restricted access to the UPC academic community 
COMBINATÒRIA I TEORIA DE GRAFTS  Parcial
Ball, Simeon Michael (Universitat Politècnica de Catalunya, 201911)
Exam
Restricted access to the UPC academic community 
Commutative semifields of rank 2 over their middle nucleus
Ball, Simeon Michael; Lavrauw, Michel (Springer, 2001)
Conference lecture
Restricted access  publisher's policyThis article is about finite commutative semifields that are of rank 2 over their middle nucleus, the largest subset of elements that is a finite field. These semifields have a direct correspondence to certain flocks of ... 
Extending small arcs to large arcs
Ball, Simeon Michael (20180301)
Article
Open AccessAn arc is a set of vectors of the kdimensional vector space over the finite field with q elements Fq , in which every subset of size k is a basis of the space, i.e. every ksubset is a set of linearly independent vectors. ... 
Forbidden subgraphs in the norm graph
Ball, Simeon Michael; Pepe, Valentina (20160406)
Article
Open AccessWe show that the norm graph with n vertices about View the MathML source edges, which contains no copy of the complete bipartite graph Kt,(t1)!+1, does not contain a copy of Kt+1,(t1)!1. 
On Segre's lemma of tangents
Ball, Simeon Michael; Csajbók, Bence (20180701)
Article
Open AccessSegre’s lemma of tangents dates back to the 1950’s when he used it in the proof of his “arc is a conic” theorem. Since then it has been used as a tool to prove results about various objects including internal nuclei, Kakeya ... 
On sets defining few ordinary planes
Ball, Simeon Michael (20170919)
Article
Open AccessLet S be a set of n points in real threedimensional space, no three collinear and not all coplanar. We prove that if the number of planes incident with exactly three points of S is less than (Formula presented.) for some ... 
On sets of points with few odd secants
Ball, Simeon Michael; Csajbok, Bence (20191010)
Article
Open AccessWe prove that, for q odd, a set of q + 2 points in the projective plane over the field with q elements has at least 2q  c odd secants, where c is a constant and an odd secant is a line incident with an odd number of points ... 
On sets of vectors of a finite vector space in which every subset of basis size is a basis II
Ball, Simeon Michael; De Beule, Jan (201210)
Article
Open AccessThis article contains a proof of the MDS conjecture for k = 2p  2. That is, that if S is a set of vectors of F k q in which every subset of S of size k is a basis, where q = p h, p is prime and q is not and k = 2p  2, ... 
On subsets of the normal rational curve
Ball, Simeon Michael; De Beule, Jan (20170601)
Article
Open AccessA normal rational curve of the (k1) dimensional projective space over Fq 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 ... 
On the graph of a function over a prime field whose small powers have bounded degree
Ball, Simeon Michael; Gács, Andras (200711)
Article
Open AccessLet $f$ be a function from a finite field ${\mathbb F}_p$ with a prime number $p$ of elements, to ${\mathbb F}_p$. In this article we consider those functions $f(X)$ for which there is a positive integer $n > 2\sqrt{p1 ...