Now showing items 1-20 of 27

• #### A bound for the maximum weight of a linear code ﻿

(2013-03-21)
Article
Open Access
It 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 ﻿

(2016-06-02)
Article
Open Access
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 D be the set of directions of the lines of L considered ...
• #### A generalisation of Sylvester's problem to higher dimensions ﻿

(2017-07-01)
Article
Open Access
In 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 ﻿

(Universitat Politècnica de Catalunya, 2019-06-03)
Exam
• #### ALA: Examen FQ: Tardor ﻿

(Universitat Politècnica de Catalunya, 2019-01-10)
Exam
• #### ALA: Examen MQ: Primavera ﻿

(Universitat Politècnica de Catalunya, 2019-03-25)
Exam
• #### ALA: Examen MQ: Tardor ﻿

(Universitat Politècnica de Catalunya, 2019-10-29)
Exam
• #### Arcs and tensors ﻿

(2019-08-01)
Article
Open Access
To an arc A of PG(k-1,q) of size q+k-1-t we associate a tensor in ¿¿k,t(A)¿¿k-1 , where ¿k,t denotes the Veronese map of degree t defined on PG(k-1,q) . As a corollary we prove that for each arc A in PG(k-1,q) of size ...
• #### Arcs in finite projective spaces ﻿

(2019-11-23)
Article
Restricted access - publisher's policy
This 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 ﻿

(Universitat Politècnica de Catalunya, 2020-01)
Exam
• #### COMBINATÒRIA I TEORIA DE GRAFTS | Parcial ﻿

(Universitat Politècnica de Catalunya, 2019-11)
Exam
• #### Commutative semifields of rank 2 over their middle nucleus ﻿

(Springer, 2001)
Conference lecture
Restricted access - publisher's policy
This 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 ﻿

(2018-03-01)
Article
Open Access
An arc is a set of vectors of the k-dimensional 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 k-subset is a set of linearly independent vectors. ...
• #### Forbidden subgraphs in the norm graph ﻿

(2016-04-06)
Article
Open Access
We show that the norm graph with n vertices about View the MathML source edges, which contains no copy of the complete bipartite graph Kt,(t-1)!+1, does not contain a copy of Kt+1,(t-1)!-1.
• #### On Segre's lemma of tangents ﻿

(2018-07-01)
Article
Open Access
Segre’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 ﻿

(2017-09-19)
Article
Open Access
Let S be a set of n points in real three-dimensional space, no three collinear and not all co-planar. 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 ﻿

(2019-10-10)
Article
Open Access
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 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 ﻿

(2012-10)
Article
Open Access
This 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 ﻿

(2017-06-01)
Article
Open Access
A normal rational curve of the (k-1) -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 ﻿

(2007-11)
Article
Open Access
Let $f$ 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{p-1 ...