arXiv subjects

Daniel Camazón Portela

Publications and source records attributed to Daniel Camazón Portela.

5 recordsLinked to original sources

arXiv2026

Linear codes arising from geometrical operation

We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords from a geometric point of view, interpreting them in terms of the combinatorial structure of the associated simplicial complex. This approach allows us to describe the minimum distance of the codes in terms of certain geometric features of the complex. Subsequently, we analyse how various topological operations on simplicial complexes affect the classical parameters of the codes. This study leads to the formulation of geometric criteria that make it possible to explicitly control and manipulate these parameters. Finally, as an application of the obtained results, we construct several families of optimal linear codes over F2 using these geometric methods. Thanks to the previously established geometric properties, we can precisely determine the parameters of these families.

cs.IT↗

arXiv2025

A generalization of Burmester-Desmedt GKE based on a non-abelian finite group action

The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast messaging or pay-per-view, could be compromised. In this work we propose a generalization of the well known group key exchange protocol proposed by Burmester and Desmedt to the non-abelian case by the use of finite group actions and we prove that the presented protocol is secure in Katz and Yung's model.

cs.CR↗

arXiv2025

The Chow ring of a sequence of point and rational curve blow-ups

Given a sequence of point and rational curve blow-ups blow-ups of smooth $3-$dimensional projective varieties $Z_{i}$ defined over an algebraically closed field $\mathit{k}$, $Z_{s}\xrightarrow{π_{s}} Z_{s-1}\xrightarrow{π_{s-1}}\cdot\cdot\cdot\xrightarrow{π_{2}} Z_{1}\xrightarrow{π_{1}} Z_{0}$, with $Z_{0}\cong\mathbb{P}^{3}$, we give an explicit presentations of the Chow ring $A^{\bullet}(Z_{s})$ of its sky. We prove that, in contrast to the case of sequences of point blow-ups, the skies of two sequences of point and rational curve blow-ups of the same length and even with the same proximity relations may have non-isomorphic Chow rings. Moreover, we explore some necessary conditions for the existence of such an isomorphism under some proximity configurations, and we apply the previous results in order to establish the allowed proximity type between two irreducible components of the exceptional divisor when both are regularly and projectively contractable.

math.AG↗

arXiv2024

Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties

The aim of this article is to give lower bounds on the parameters of algebraic geometric error-correcting codes constructed from projective bundles over Deligne--Lusztig surfaces. The methods based on an intensive use of the intersection theory allow us to extend the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. General bounds are obtained for the case of projective bundles of rank $2$ over standard Deligne-Lusztig surfaces, and some explicit examples coming from surfaces of type $A_{2}$ and ${}^{2}A_{4}$ are given.

cs.IT↗

arXiv2023

The Chow ring of a sequence of point blow-ups

Given a sequence of point blow-ups of smooth n-dimensional projective varieties $Z_{i}$ defined over an algebraically closed field k, $Z_{s}\rightarrow Z_{s-1}\rightarrow ...\rightarrow Z_{1}\rightarrow Z_{0}$, we give two presentations of the Chow ring of its sky $A^{\bullet}(Z_{s})$. The first one using the classes of the total transforms of the exceptional components as generators and the second one using the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of final divisor of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles of its sky $A_{0}(Z_{s})$.

math.AG↗