Lattices Associated with Octonion Algebras
Abstract
In this paper, we propose a construction of lattices in dimension 8n via octonion orders over a totally real number field. To show the potential of this construction, we present rotated versions of $E_8$, $\Lambda_{16}$, the densest known lattices in these dimensions and a lattice with the same density of the Barnes-Wall lattice in dimension 32. Perspectives applications of these lattices based on octonion algebras are in lattice-based cryptography and lattice coding for MIMO and MISO channels.
Published
03-08-2018
How to Cite
Brasil Junior, N., Benedito, C., & Costa, S. (2018). Lattices Associated with Octonion Algebras. Journal of Communication and Information Systems, 33(1). https://doi.org/10.14209/jcis.2018.24
Issue
Section
Regular Papers
Copyright (c) 2018 Nelson Gomes Brasil Junior, Cintya Wink de Oliveira Benedito, Sueli Irene Rodrigues Costa
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