Lattices from codes over ${\mathbb{Z}}_q$: Generalization of Constructions $D$, $D^{\prime }$ and $\overline{D}$

Eleonesio Strey, Sueli I. R. Costa

In this paper, we extend the lattice Constructions $D$, $D^{\prime }$ and $\overline{D}$ $($this latter is also known as Forney's code formula$)$ from codes over ${\mathbb{F}}_p$ to linear co…