Rotated DnD_n-lattices in dimensions power of 33

In this work, we present constructions of families of rotated $D_n$-lattices which may be good forsignal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $\mathbb{Z} \oplus \mathcal{A}_{2}^{k}$ lattices, where $\mathcal{A}_{2}^{k}$ is a direct sum of $k=\frac{3^{r-1}-1}{2}$ copies of the $A_2$-lattice, using free $\mathbb{Z}$-modules in $\mathbb{Z}[\zeta_{3^{r}}+\zeta_{3^{r}}^{-1}]$

Reticulados ideais via corpos abelianos

O objetivo deste trabalho é o estudo de reticulados ideais. Neste estudo enfatizamos o artigo Lattices and Number Fields de Eva Bayer-Fluckiger, que apresenta alguns reticulados ideais com as mesmas propriedades que os reticulados Ap¡1, p primo, D4, E6, E8, K12 e ¤24.The aim of this work is the study of ideal lattices. In this study we stress a Eva Bayer-Fluckiger's article \Lattices and Number Fields with presents some ideal lattices with same properties that lattices Ap¡1, p prime number, D4, E6, E8, K12 e ¤24.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Q-ary and algebraic lattices

Orientador: Sueli Irene Rodrigues CostaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação CientificaResumo: O uso de códigos e reticulados em teoria da informação e na "chamada criptografia pós-quântica" vem sendo cada vez mais explorado. Neste trabalho estudamos temas relacionados a estas duas vertentes. A análise de reticulados foi feita via as métricas euclidiana e da soma. Para a métrica euclidiana, estudamos um algoritmo que procura pela treliça mínima de um reticulado com sub-reticulado ortogonal. No caso bidimensional foi possível caracterizar todos os sub-reticulados ortogonais de um reticulado racional qualquer. No estudo de reticulados via métrica da soma, trabalhamos com duas relações entre códigos e reticulados, conhecidas como "Construção A" e "Construção B". Generalizamos a Construção B para uma classe de códigos q-ários... Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digitalAbstract: The use of codes and lattices in Information Theory and in the so-called "Post-quantum Cryptography" has been increasingly explored. In this work we have studied topics related to these two aspects. The analysis of lattices was made via Euclidean and sum metrics. For the Euclidean metric we studied an algorithm that searches for a minimum trellis of a lattice with orthogonal sublattice. In the two-dimensional case it has been possible to characterize all orthogonal sublattices of any rational lattice. In the study of lattices via sum metric, we worked with two relations between codes and lattices, the so-called "Construction A " and "Construction B". We generalized Construction B for the class of q-ary codes...Note: The complete abstract is available with the full electronic documentDoutoradoMatematicaDoutor em Matemátic

Rotated DnD_n-lattices in dimensions power of 33

In this work, we present constructions of families of rotated $D_n$-lattices which may be good for signal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $\mathbb{Z} \oplus \mathcal{A}_{2}^{k}$ lattices, where $\mathcal{A}_{2}^{k}$ is a direct sum of $k=\frac{3^{r-1}-1}{2}$ copies of the $A_2$-lattice, using free $\mathbb{Z}$-modules in $\mathbb{Z}[\zeta_{3^{r}}+\zeta_{3^{r}}^{-1}]$

Codes and lattices in the l(p) metric

Codes and associated lattices are studied in the l(p) metric, particularly in the l(1) (Lee) and the l(infinity) (maximum) distances. Discussions and results on decoding processes, classification and analysis of perfect or dense codes in these metrics are presented.Univ Estadual Campinas, Inst Math, Campinas, SP, BrazilUniv Fed Sao Paulo, Inst Sci & Technol, Sao Paulo, BrazilUniv Estadual Campinas, Sch Appl Sci, Campinas, SP, BrazilUniv Fed Sao Paulo, Inst Sci & Technol, Sao Paulo, BrazilWeb of Scienc

NEOTROPICAL ALIEN MAMMALS: a data set of occurrence and abundance of alien mammals in the Neotropics

Biological invasion is one of the main threats to native biodiversity. For a species to become invasive, it must be voluntarily or involuntarily introduced by humans into a nonnative habitat. Mammals were among first taxa to be introduced worldwide for game, meat, and labor, yet the number of species introduced in the Neotropics remains unknown. In this data set, we make available occurrence and abundance data on mammal species that (1) transposed a geographical barrier and (2) were voluntarily or involuntarily introduced by humans into the Neotropics. Our data set is composed of 73,738 historical and current georeferenced records on alien mammal species of which around 96% correspond to occurrence data on 77 species belonging to eight orders and 26 families. Data cover 26 continental countries in the Neotropics, ranging from Mexico and its frontier regions (southern Florida and coastal-central Florida in the southeast United States) to Argentina, Paraguay, Chile, and Uruguay, and the 13 countries of Caribbean islands. Our data set also includes neotropical species (e.g., Callithrix sp., Myocastor coypus, Nasua nasua) considered alien in particular areas of Neotropics. The most numerous species in terms of records are from Bos sp. (n = 37,782), Sus scrofa (n = 6,730), and Canis familiaris (n = 10,084); 17 species were represented by only one record (e.g., Syncerus caffer, Cervus timorensis, Cervus unicolor, Canis latrans). Primates have the highest number of species in the data set (n = 20 species), partly because of uncertainties regarding taxonomic identification of the genera Callithrix, which includes the species Callithrix aurita, Callithrix flaviceps, Callithrix geoffroyi, Callithrix jacchus, Callithrix kuhlii, Callithrix penicillata, and their hybrids. This unique data set will be a valuable source of information on invasion risk assessments, biodiversity redistribution and conservation-related research. There are no copyright restrictions. Please cite this data paper when using the data in publications. We also request that researchers and teachers inform us on how they are using the data