Robson Ricardo de Araujo

• Abstract

  This research project consists of an introductory study on algebraic number theory, its articulations with lattice theory and an overview of some of its theoretical and practical applications. The topics covered involve studies on algebraic numbers, number fields, rings of integers, quadratic and cyclotomic fields, ramification of ideals, lattices, Minkowski embedding, elliptic curves, am…

  Algebraic numbers, lattices and applications, BP.IC

• Abstract

  This work consists of a study, at the scientific initiation level, on basic aspects of finite field theory and its applications to algebraic error-correcting codes, with emphasis on linear codes. In particular, this project proposes a study on cyclic codes, BCH codes, Reed-Solomon codes, and LDPC codes. (AU)

  Introduction to finite fields and to algebraic error-correcting codes, BP.IC

• Abstract

  This work is a study, at the undergraduate level, about basic aspects of algebraic number theory and its connections with lattice theory, including approaches to integral and algebraic elements, number fields, rings of integers, cyclotomic fields, Minkowski embedding, algebraic lattices, decomposition of ideals, among others. (AU)

  A study about algebraic number theory and lattices, BP.IC

(Only some records are available in English at this moment)

• Abstract

  Lattices, which are discrete additive subgroups of Rn, have been studied for centuries and play a crucial role in various fields, including optimization, telecommunications, and cryptography. These structures are renowned for their significance associated with important mathematical problems, such as sphere packing. For decades, lattice codes have been proposed and used for signal transmi…

  Investigation of problems related to lattice-based cryptography using algebraic number theory, BE.PQ