FOUR-DIMENSIONAL LATTICES FROM $\mathbb Q(\sqrt{2},\sqrt{5})$
J. Carmelo Interlando1, Trajano Pires da Nóbrega Neto2
José Valter Lopes Nunes3, José Othon Dantas Lopes4
1Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182-7720, USA
2Department of Mathematics
São Paulo State University
São José do Rio Preto, SP 15054-000, BRAZIL
3Department of Mathematics
Federal University of Ceará
Fortaleza, CE 60455-900, BRAZIL
4Department of Mathematics
Federal University of Ceará
Fortaleza, CE 60455-900, BRAZIL

Abstract

Four-dimensional lattices with block circulant generator matrices are constructed from submodules of the ring of integers of the totally real number field $\mathbb Q(\sqrt{2},\sqrt{5})$. The obtained lattices are of full diversity and their sphere packing densities are the highest known for the given relative minimum product distances.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 5
Year: 2017

DOI: 10.12732/ijam.v30i5.4

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