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Random Ensembles of Lattices From Generalized Reductions

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Autor(es):
Campello, Antonio
Número total de Autores: 1
Tipo de documento: Artigo Científico
Fonte: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 64, n. 7, p. 5231-5239, JUL 2018.
Citações Web of Science: 2
Resumo

We propose a general framework to study constructions of Euclidean lattices from linear codes over finite fields. In particular, we prove general conditions for an ensemble constructed using linear codes to contain dense lattices (i.e., with packing density comparable to the Minkowski-Hlawka lower bound). Specializing to number field lattices, we obtain a number of interesting corollaries - for instance, the best known packing density of ideal lattices, and an elementary codingtheoretic construction of asymptotically dense Hurwitz lattices. All results are algorithmically effective, in the sense that, for any dimension, a finite family containing dense lattices is exhibited. For suitable constructions based on Craig's lattices, this family is smaller, in terms of alphabet-size, than previous ensembles in the literature. (AU)

Processo FAPESP: 14/20602-8 - Reticulados e Teoria da Informação com múltiplos usuários
Beneficiário:Antonio Carlos de Andrade Campello Junior
Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado