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.

Arithmetic fuchsian groups and space time block codes

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

Mandibular Angle Fracture Treated With New Three-Dimensional Grid Miniplate

Fractures of the mandibular angle deserve particular attention because they represent the highest percentage of mandibular fractures and have the highest postsurgical complication rate, making them the most challenging and unpredictable mandibular fractures to treat. Despite the evolution in the treatment of maxillofacial trauma and fixation methods, no single treatment modality has been revealed to be ideal for mandibular angle fractures. Several methods of internal fixation have been studied with great variation in complications rates, especially postoperative infections. Recently, new studies have shown reduction of postsurgical complications rates using three-dimensional plates to treat mandibular angle fractures. Nevertheless, only few surgeons have used this type of plate for the treatment of mandibular angle fractures. The aim of this clinical report was to describe a case of a patient with a mandibular angle fracture treated by an intraoral approach and a three-dimensional rectangular grid miniplate with 4 holes, which was stabilized with monocortical screws. The authors show a follow-up of 8 months, without infection and with occlusal stability.

Use of Rectangular Grid Miniplates for Fracture Fixation at the Mandibular Angle

Purpose: The aim of this study was to evaluate the clinical outcome of patients with mandibular angle fractures treated by intraoral access and a rectangular grid miniplate with 4 holes and stabilized with monocortical screws.Patients and Methods: This study included 45 patients with mandibular angle fractures from the Department of Oral and Maxillofacial Surgery São Paulo State University, Araraquara, Brazil, and from the Clinic of Oral and Maxillofacial Surgery at the University of Frankfurt, Germany. The 45 fractures of the mandibular angle were treated with a rectangular grid miniplate of a 2.0-mm system by an intraoral approach with monocortical screws. Clinical evaluations were postoperatively performed at 15 and 30 days and 3 and 6 months, and the complications encountered were recorded and treated.Results: The infection rate was 4.44% (2 patients), and in 1 patient it was necessary to replace hardware. This patient also had a fracture of the left mandibular body; 3 patients (6.66%) had minor occlusal changes that have been resolved with small occlusal adjustments. Before surgery, 15 patients (33.33%) presented with hypoesthesia of the inferior alveolar nerve; 4 (8.88%) had this change until the last clinical control, at 6 months.Conclusions: The rectangular grid miniplate used in this study was stable for the treatment of simple mandibular angle fractures through intraoral access, with low complication rates, easy handling, and easy adjustment, with a low cost. Concomitant mandibular fracture may increase the rate of complications. This plate should be indicated in fractures with sufficient interfragmentaty contact. (C) 2011 American Association of Oral and Maxillofacial Surgeons J Oral Maxillofac Surg 69:1436-1441, 2011

Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Goppa and Srivastava codes over finite rings

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

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric.

CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

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

Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding

For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B[X; 1/2; Z(0)] In this study we developed a construction technique of cyclic codes through a semigroup ring B[X; 1/2(2)Z(0)] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B[X; 1/2(2)Z(0)]. Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense. Published by Elsevier Ltd

Geometrically uniform hyperbolic codes

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes.

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

Hamming and Reed-Solomon codes over certain rings

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

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.

Two-way regionalized classification of multivariate datasets and its application to the assessment of hydrodynamic dispersion

Zones of mixing between shallow groundwaters of different composition were unravelled by two-way regionalized classification, a technique based on correspondence analysis (CA), cluster analysis (ClA) and discriminant analysis (DA), aided by gridding, map-overlay and contouring tools. The shallow groundwaters are from a granitoid plutonite in the Funda o region (central Portugal). Correspondence analysis detected three natural clusters in the working dataset: 1, weathering; 2, domestic effluents; 3, fertilizers. Cluster analysis set an alternative distribution of the samples by the three clusters. Group memberships obtained by correspondence analysis and by cluster analysis were optimized by discriminant analysis, gridded memberships as follows: codes 1, 2 or 3 were used when classification by correspondence analysis and cluster analysis produced the same results; code 0 when the grid node was first assigned to cluster 1 and then to cluster 2 or vice versa (mixing between weathering and effluents); code 4 in the other cases (mixing between agriculture and the other influences). Code-3 areas were systematically surrounded by code-4 areas, an observation attributed to hydrodynamic dispersion. Accordingly, the extent of code-4 areas in two orthogonal directions was assumed proportional to the longitudinal and transverse dispersivities of local soils. The results (0.7-16.8 and 0.4-4.3 m, respectively) are acceptable at the macroscopic scale. The ratios between longitudinal and transverse dispersivities (1.2-11.1) are also in agreement with results obtained by other studies.

Performance of an operating high energy physics data grid: DOSAR-Grid

The DO experiment at Fermilab's Tevatron will record several petabytes of data over the next five years in pursuing the goals of understanding nature and searching for the origin of mass. Computing resources required to analyze these data far exceed capabilities of any one institution. Moreover, the widely scattered geographical distribution of DO collaborators poses further serious difficulties for optimal use of human and computing resources. These difficulties will exacerbate in future high energy physics experiments, like the LHC. The computing grid has long been recognized as a solution to these problems. This technology is being made a more immediate reality to end users in DO by developing a grid in the DO Southern Analysis Region (DOSAR), DOSAR-Grid, using a available resources within it and a home-grown local task manager, McFarm. We will present the architecture in which the DOSAR-Grid is implemented, the use of technology and the functionality of the grid, and the experience from operating the grid in simulation, reprocessing and data analyses for a currently running HEP experiment.