TY - JOUR AU - Brasil Junior, Nelson Gomes AU - Benedito, Cintya Wink de Oliveira AU - Costa, Sueli Irene Rodrigues PY - 2018/08/03 Y2 - 2024/03/29 TI - Lattices Associated with Octonion Algebras JF - Journal of Communication and Information Systems JA - Journal of Communication and Information Systems VL - 33 IS - 1 SE - Regular Papers DO - 10.14209/jcis.2018.24 UR - https://jcis.sbrt.org.br/jcis/article/view/549 SP - AB - <p>In this paper, we propose a construction of lattices in&nbsp;dimension 8n via octonion orders over a totally real number field.&nbsp;To show the potential of this construction, we present rotated&nbsp;versions of $E_8$,&nbsp;$\Lambda_{16}$, the&nbsp; densest known lattices in these dimensions&nbsp;and a lattice with the same density of the Barnes-Wall lattice in&nbsp;dimension 32. Perspectives applications of these lattices based on&nbsp;octonion algebras are in lattice-based cryptography and lattice&nbsp;coding for MIMO and MISO channels.</p> ER -