| Texto completo | |
| Autor(es): |
Strapasson, Joao Eloir
;
De Araujo, Robson Ricardo
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING; v. N/A, p. 12-pg., 2026-01-07. |
| Resumo | |
Lattices are discrete additive subgroups of R-n known to be useful in finding solutions to important mathematical problems, such as the Sphere Packing Problem, and in applications for coding theory and post-quantum cryptography. In particular, well-rounded lattices have been considered for data transmission on Wiretap channels. A lattice obtained as an image of a free Z-submodule of the ring of algebraic integers of a number field through the canonical embedding, or a twisted version of it, is called an algebraic lattice. In 2012, Fukshansky and Petersen showed that an algebraic lattice obtained as image of the whole ring of algebraic integers of a number field K through the canonical embedding is well-rounded if and only if K is a cyclotomic field. In this work, we prove that the lattice obtained as image of the ring of algebraic integers of the maximal real subfield of the 4q-th cyclotomic field via some twisted embedding is well-rounded for any odd integer number q. (AU) | |
| Processo FAPESP: | 20/09838-0 - BI0S - Brazilian Institute of Data Science |
| Beneficiário: | João Marcos Travassos Romano |
| Modalidade de apoio: | Auxílio à Pesquisa - Programa Centros de Pesquisa Aplicada |
| Processo FAPESP: | 22/12667-9 - Números algébricos, reticulados e aplicações |
| Beneficiário: | Cleber Luiz de Oliveira Santos |
| Modalidade de apoio: | Bolsas no Brasil - Iniciação Científica |