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.

Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

Optimal pest control problem in population dynamics

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

Possibility of collision between co-orbital asteroids and the Earth

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

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.

A method for improving the code rate and error correction capability of a cyclic code

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Perspectivas históricas da pesquisa operacional

Pós-graduação em Educação Matemática - IGCE

Métodos numéricos para o retoque digital

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo de métodos numéricos para eliminação de ruídos em imagens digitais

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Propriedades e convergência de certas fórmulas de quadratura interpolatórias

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelos matemáticos para o retoque digital de imagens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Leis de Conservação Hiperbólicas 2D com Termo Fonte Stiff

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

Desenvolvimento de um método numérico para simular escoamentos viscoelásticos axissimétricos com superfícies livres: Modelo PTT

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

Zeros de Polinômios Perturbados

Pós-graduação em Matematica Aplicada e Computacional - FCT