Lattices Associated with Octonion Algebras

Authors

  • Nelson Gomes Brasil Junior Instituto de Matemática, Estatística e Computação Científica -- IMECC/Unicamp
  • Cintya Wink de Oliveira Benedito Universidade Estadual Paulista, Unesp – São João da Boa Vista-SP
  • Sueli Irene Rodrigues Costa Instituto de Matemática, Estatística e Computação Científica -- IMECC/Unicamp

DOI:

https://doi.org/10.14209/jcis.2018.24

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.

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Published

2018-08-03

How to Cite

Brasil Junior, N. G., Benedito, C. W. de O., & Costa, S. I. R. (2018). Lattices Associated with Octonion Algebras. Journal of Communication and Information Systems, 33(1). https://doi.org/10.14209/jcis.2018.24

Issue

Vol. 33 No. 1 (2018)

Section

Regular Papers

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Received 2018-02-28
Accepted 2018-07-10
Published 2018-08-03