Hamming and Reed-Solomon codes over certain rings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structural refinement and photoluminescence properties of irregular cube-like (Ca-1_Cu-x(x))TiO3 microcrystals synthesized by the microwave-hydrothermal method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Revendo os códigos hamming e CRC para tratar com erros na transmissão de dados

This article has the purpose to review the main codes used to detect and correct errors in data communication specifically in the computer's network. The Hamming's code and the Ciclic Redundancy Code (CRC) are presented as the focus of this article as well as CRC hardware implementation. Each code is reviewed in details in order to fill the gaps in the literature and to make it accessible to the computer science and engineering students as well as to anyone who may be interested in learning the technique to treat error in data communication.

Structural refinement and photoluminescence properties of cube-like (Ca 1-xCu x)TiO 3 crystals synthesized by the microwave-hydrothermal method

In this work, (Ca 1-xCu x)TiO 3 crystals with (x = 0, 0.01 and 0.02), labeled as CTO, CCTO1 and CCTO2, were synthesized by the microwave-hydrothermal method at 140°C for 32 min. XRD patterns (Fig. 1), Rietveld refinement and FT-Raman spectroscopy indicated that these crystals present orthorhombic structure Pbnm. Micro-Raman and XANES spectra suggested that the substitution of Ca by Cu in A-site promoted a displacement of the [TiO6]-[TiO6] clusters adjacent from its symmetric center, which leads distortions on the [CaO 12] clusters neighboring and consequently cause the strains into the CaTiO3 lattice. FE-SEM images showed that these crystals have an irregular shape as cube like probably indicating an Ostwald-ripening and self-assemble as dominant mechanisms to crystals growth. The powders presented an intense PL blue-emission.

Long-range and short-range structures of cube-like shape SrTiO3 powders: microwave-assisted hydrothermal synthesis and photocatalytic activity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fine root isotropy in Eucalyptus grandis plantations. Towards the prediction of root length densities from root counts on trench walls

The objectives of the study were to assess changes in fine root anisotropy and specific root lengths throughout the development of Eucalyptus grandis ( W. Hill ex Maiden) plantations and to establish a predictive model of root length density (RLD) from root intercept counts on trench walls. Fine root densities (<1 mm in diameter) were studied in 6-, 12-, 22-, 28-, 54-, 68- and 72-month-old E. grandis plantations established on deep Ferralsols in southern Brazil. Fine root intercepts were counted on 3 faces of 90-198 soil cubes (1 dm(3) in volume) in each stand and fine root lengths (L) were measured inside 576 soil cubes, sampled between the depths of 10 cm and 290 cm. The number of fine root intercepts was counted on one vertical face perpendicular to the planting row (N(t)), one vertical face parallel to the planting row (N(l)) and one horizontal face (N(h)), for each soil cube sampled. An overall isotropy of fine roots was shown by paired Student's t-tests between the numbers of fine roots intersecting each face of soil cubes at most stand ages and soil depths. Specific root lengths decreased with stand age in the upper soil layers and tended to increase in deep soil layers at the end of the rotation. A linear regression established between N(t) and L for all the soil cubes sampled accounted for 36% of the variability of L. Such a regression computed for mean Nt and L values at each sampling depth and stand age explained only 55% of the variability, as a result of large differences in the relationship between L and Nt depending on stand productivity. The equation RLD=1.89*LAI*N(t), where LAI was the stand leaf area index (m(2) m(-2)) and Nt was expressed as the number of root intercepts per cm(2), made it possible to predict accurately (R(2)=0.84) and without bias the mean RLDs (cm cm(-3)) per depth in each stand, for the whole data set of 576 soil cubes sampled between 2 years of age and the end of the rotation.

Preparation, characterization and application of a nanostructured composite: Octakis(cyanopropyldimethylsiloxy)octasilsesquioxane

Octakis(cyanopropyldimethylsiloxy)octasilsesquioxane was prepared and characterized by C-13, Si-29 NMR (MAS), SEM, FF-IR, XRD and thermogravimetric techniques. The four groups alpha, beta, gamma, kappa (to the terminal silicon atom), associated with an acrylonitrile, were clearly seen in the C-13 NMR (alpha-CH2 at 17.9; P-CH2 at 31.3; gamma-CH, at 50.4; K-C N at 59.0 ppm). The Si-29 NMR spectrum of the final product, exhibits only Q type silicon signal, ascribed to Q(4) (-118.0 ppm). The presence of acrylonittile substituted for octameric cube confers a relative change phase and thermal stability to the material. With regard to the applications for this new material, it was intended, in this case, to react with Na-2[Fe(CN)(5)NH3] by chemical substitution. This composite was incorporated into a carbon paste electrode and the electrochemical studies were performed by cyclic voltammetry. The cyclic voltammogram of the modified graphite paste electrode, showed one redox couples with formal potential (E-1/2(ox)) = 0.24 V versus SCE. (c) 2006 Elsevier B.V. All rights reserved.

Critical temperature for first-order phase transitions in confined systems

We consider the Euclidean D-dimensional -lambda vertical bar phi vertical bar(4)+eta vertical bar rho vertical bar(6) (lambda,eta > 0) model with d (d <= D) compactified dimensions. Introducing temperature by means of the Ginzburg-Landau prescription in the mass term of the Hamiltonian, this model can be interpreted as describing a first-order phase transition for a system in a region of the D-dimensional space, limited by d pairs of parallel planes, orthogonal to the coordinates axis x(1), x(2),..., x(d). The planes in each pair are separated by distances L-1, L-2, ... , L-d. We obtain an expression for the transition temperature as a function of the size of the system, T-c({L-i}), i = 1, 2, ..., d. For D = 3 we particularize this formula, taking L-1 = L-2 = ... = L-d = L for the physically interesting cases d = 1 (a film), d = 2 (an infinitely long wire having a square cross-section), and for d = 3 (a cube). For completeness, the corresponding formulas for second-order transitions are also presented. Comparison with experimental data for superconducting films and wires shows qualitative agreement with our theoretical expressions.

Photoluminescence properties of PZT 52/48 synthesized by microwave hydrothermal method using PVA with template

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Photoluminescence properties and synthesis of a PZT mesostructure obtained by the microwave-assisted hydrothermal method

Micro-cube-shaped lead zirconate titanate was synthesized using the microwave-assisted hydrothermal method. Photoluminescence and field emission scanning electron microscopy were used for monitoring the formation of mesocrystals. Based on these results, a growth mechanism was then proposed which involved nanoparticle aggregation, nanoplate self-assembly on specific architecture and the final formation of mesoscopic micro-cube-shaped lead zirconate titanate. (C) 2011 Elsevier B. V. All rights reserved.

Relating propelinear and binary G-linear codes

In this paper we establish the connections between two different extensions of Z(4)-linearity for binary Hamming spaces, We present both notions - propelinearity and G-linearity - in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and translation-invariant propelinear codes are G-linear codes. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Optimum-Path Forest Classifier for Large Scale Biometric Applications

This paper addresses biometric identification using large databases, in particular, iris databases. In such applications, it is critical to have low response time, while maintaining an acceptable recognition rate. Thus, the trade-off between speed and accuracy must be evaluated for processing and recognition parts of an identification system. In this paper, a graph-based framework for pattern recognition, called Optimum-Path Forest (OPF), is utilized as a classifier in a pre-developed iris recognition system. The aim of this paper is to verify the effectiveness of OPF in the field of iris recognition, and its performance for various scale iris databases. The existing Gauss-Laguerre Wavelet based coding scheme is used for iris encoding. The performance of the OPF and two other - Hamming and Bayesian - classifiers, is compared using small, medium, and large-scale databases. Such a comparison shows that the OPF has faster response for large-scale databases, thus performing better than the more accurate, but slower, classifiers.

A Fast Large Scale Iris Database Classification with Optimum-Path Forest Technique: A Case Study

Majority of biometric researchers focus on the accuracy of matching using biometrics databases, including iris databases, while the scalability and speed issues have been neglected. In the applications such as identification in airports and borders, it is critical for the identification system to have low-time response. In this paper, a graph-based framework for pattern recognition, called Optimum-Path Forest (OPF), is utilized as a classifier in a pre-developed iris recognition system. The aim of this paper is to verify the effectiveness of OPF in the field of iris recognition, and its performance for various scale iris databases. This paper investigates several classifiers, which are widely used in iris recognition papers, and the response time along with accuracy. The existing Gauss-Laguerre Wavelet based iris coding scheme, which shows perfect discrimination with rotary Hamming distance classifier, is used for iris coding. The performance of classifiers is compared using small, medium, and large scale databases. Such comparison shows that OPF has faster response for large scale database, thus performing better than more accurate but slower Bayesian classifier.

Line based camera calibration in machine vision dynamic applications

The problem of dynamic camera calibration considering moving objects in close range environments using straight lines as references is addressed. A mathematical model for the correspondence of a straight line in the object and image spaces is discussed. This model is based on the equivalence between the vector normal to the interpretation plane in the image space and the vector normal to the rotated interpretation plane in the object space. In order to solve the dynamic camera calibration, Kalman Filtering is applied; an iterative process based on the recursive property of the Kalman Filter is defined, using the sequentially estimated camera orientation parameters to feedback the feature extraction process in the image. For the dynamic case, e.g. an image sequence of a moving object, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and based on the system model parameters with good quality, for each instant of an image sequence. The proposed approach was tested with simulated and real data. Experiments with real data were carried out in a controlled environment, considering a sequence of images of a moving cube in a linear trajectory over a flat surface.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.