Reticulados associados a álgebra dos octônios

Nelson G. Brasil Jr, Cintya W. O. Benedito, Sueli I. R. Costa

DOI: 10.14209/sbrt.2017.136

Evento: XXXV Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2017)

Keywords: Ideal Lattices Algebraic Number Theory Division Algebra Octonion Algebra

Abstract

In this paper, we propose a construction of lattices in dimension 8n via orders in an octonion algebra over a totally real number field. Using this construction, we present rotated versions of E8 and Λ16 lattices that are the densest lattices in dimension 8 and 16, respectively.

Download