Multilevel lattice codes, such as those associated to Constructions $C$, $\overline{D}$, 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 matrices, expressions and bounds for the lattice 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.

翻译：多级格码，例如与构造$C$、$\overline{D}$、D和D'相关的码，在通信中具有重要应用。本文研究了由q元线性码通过构造D和D'获得的格的一些性质。推导了与构造A、生成矩阵、表达式以及格体积和最小距离的界之间的关系。此外，还给出了关于二元和p元线性码（p为素数）的构造与译码的先前结果的扩展。