Lattices Associated with Octonion Algebras
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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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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
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