Computing coset leaders and leader codewords of binary codes

In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted by $\mathrm L(\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation stablished between zero neighbours and leader codewords

On the number of nonequivalent propelinear extended perfect codes

The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation

Gauge theory of self-similar system

On the basis of a dilatation invariant Lagrangian, governed equations are determined for probability density and gauge potential of the non-stationary self-similar stochastic system. It is shown that an automodel regime is observed at small time interval determined by the Tsallis' parameter $q>1$. An exponential falling down happens at large time where the dilatation parameter and the partial scale tend to constant values.Comment: 8 pages, LaTe

Neighbour transitivity on codes in Hamming graphs

We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming graph}. In this setting a \emph{neighbour} of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the property that some group of automorphisms acts transitively on the \emph{set of neighbours} of the code. We call these codes \emph{neighbour transitive}. We obtain sufficient conditions for a neighbour transitive group to fix the code setwise. Moreover, we construct an infinite family of neighbour transitive codes, with \emph{minimum distance} $\delta=4$, where this is not the case. That is to say, knowledge of even the complete set of code neighbours does not determine the code

Two loops calculation in chiral perturbation theory and the unitarization program of current algebra

In this paper we compare two loop Chiral Perturbation Theory (ChPT) calculation of pion-pion scattering with the unitarity second order correction to the current algebra soft-pion theorem. It is shown that both methods lead to the same analytic structure for the scattering amplitude.Comment: 13 pages, Revtex 3.0, no figures, submitted to Phys. Lett.

New family of potentials with analytical twiston-like solutions

In this letter we present a new approach to find analytical twiston models. The effective two-field model was constructed by a non-trivial combination of two one field systems. In such an approach we successfully build analytical models which are satisfied by a combination of two defect-like solutions, where one is responsible to twist the molecular chain by $180^{\,0}$, while the other implies in a longitudinal movement. Such a longitudinal movement can be fitted to have the size of the distance between adjacent molecular groups. The procedure works nicely and can be used to describe the dynamics of several other molecular chains.Comment: 7 pages, 3 figure

Privacy-Preserving Protocols for Vehicular Transport Systems

La present tesi es centra en la privadesa dels ciutadans com a usuaris de mitjans de transport vehiculars dins del marc d'una e-society. En concret, les contribucions de la tesi es focalitzen en les subcategories d'estacionament de vehicles privats en zones públiques regulades i en la realització de transbordaments entre línies intercomunicades en l'àmbit del transport públic. Una anàlisi acurada de les dades recopilades pels proveedors d'aquests serveis, sobre un determinat usuari, pot proporcionar informació personal sensible com per exemple: horari laboral, professió, hobbies, problemes de salut, tendències polítiques, inclinacions sexuals, etc. Tot i que existeixin lleis, com l'europea GDPR, que obliguin a utilitzar les dades recollides de forma correcta per part dels proveedors de serveis, ja sigui a causa d'un atac informàtic o per una filtració interna, aquestes dades poden ser utilitzades per finalitats il·legals. Per tant, el disseny protocols que garanteixin la privadesa dels ciutadans que formen part d'una e-society esdevé una tasca de gran importància.La presente tesis se centra en la privacidad de los ciudadanos en el transporte vehicular dentro del marco de una e-society. En concreto, las contribuciones de la tesis se centran en las subcategorías de estacionamiento de vehículos privados en zonas públicas reguladas y en la realización de transbordos entre líneas interconectadas en el ámbito del transporte público. Una análisi acurada de los datos recopilados por los proveedores de los servicios, sobre un determinado usuario, puede proporcionar información personal sensible como por ejemplo: horario laboral, profesión, hobbies, problemas de salud, tendencias políticas, inclinaciones sexuales, etc. A pesar que hay leyes, como la europea GDPR, que obligan a usar de forma correcta los datos recopilados por parte de los proveedores de servicios, ya sea por un ataque informático o por una filtración interna, estos datos pueden utilizarse para fines ilegales. Por lo tanto, es vital diseñar protocolos que garanticen la privacidad de los ciudadanos que forman parte de una e-society.This thesis is focused on the privacy of citizens while using vehicular transport systems within an e-society frame. Specifically, the thesis contributes to two subcategories. The first one refers to pay-by-phone systems for parking vehicles in regulated public areas. The second one is about the use of e-tickets in public transport systems allowing transfers between connecting lines. A careful analysis of data collected by service providers can provide sensitive personal information such as: work schedule, profession, hobbies, health problems, political tendencies, sexual inclinations, etc. Although the law, like the European GDPR, requires the correct use of the data collected by service providers, data can be used for illegal purposes after being stolen as a result of a cyber-attack or after being leaked by an internal dishonest employee. Therefore, the design of privacy-preserving solutions for mobility-based services is mandatory in the e-society

Treatment of bimodality in proficiency test of pH in bioethanol matrix

The pH value in bioethanol is a quality control parameter related to its acidity and to the corrosiveness of vehicle engines when it is used as fuel. In order to verify the comparability and reliability of the measurement of pH in bioethanol matrix among some experienced chemical laboratories, reference material (RM) of bioethanol developed by Inmetro - the Brazilian National Metrology Institute - was used in a proficiency testing (PT) scheme. There was a difference of more than one unit in the value of the pH measured due to the type of internal filling electrolytic solutions (potassium chloride, KCl or lithium chloride, LiCl) from the commercial pH combination electrodes used by the participant laboratories. Therefore, bimodal distribution has occurred from the data of this PT scheme. This work aims to present the possibilities that a PT scheme provider can use to overcome the bimodality problem. Data from the PT of pH in bioethanol were treated by two different statistical approaches: kernel density model and the mixture of distributions. Application of these statistical treatments improved the initial diagnoses of PT provider, by solving bimodality problem and contributing for a better performance evaluation in measuring pH of bioethanol.Comment: 20 pages, 6 figures, Accepted for publication in Accreditation and Quality Assurance (ACQUAL