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.

翻译：多级格码（例如与构造$C$、$\overline{\mbox{D}}$、D和D'相关联的格码）在通信中具有重要应用。本文研究了基于q元线性码通过构造D和D'所得格的一些性质。推导了与构造A、生成矩阵的联系，以及体积和最小距离的表达式与界。此外，还给出了对二进制和p元（p为素数）线性码的构造及译码相关前期成果的推广。