On Lattice Constructions D and D' from q-ary Linear Codes

Multilevel lattice codes, such as the associated to Constructions $C$, $\overline{\mbox{D}}$, D and D', have relevant applications in communications. In this paper, we investigate some properties of lattices obtained via Constructions D and D' from $q$-ary linear codes. Connections with Construction A, generator matrix, expressions and bounds for volume and minimum distances are derived. Extensions of previous results regarding construction and decoding of binary and $p$-ary linear codes ($p$ prime) are also presented.