A ternary construction of lattices

Abstract

In this paper we propose a general ternary construction of lattices from three rows and ternary codes. Most laminated lattices and Kappa lattices in ${\mathbf{R}}^n$, $n\le 24$ can be recovered from our tenary construction naturally. This ternary construction of lattices can be used to generate many new "sub-optimal" lattices of low dimensions.Based on this ternary construction new extremal even lattices of dimensions $32,40$ and $48$ are also constructed.

59 pages, new extremal even lattices added

References in corpus (2)

• New upper bounds on sphere packings I
• The unreasonable effectiveness of the tensor product