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 ${\bf R}^n$, $n\leq 24$ 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.