Multilevel lattice codes, such as the 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：多层格码（例如与构造C、$\overline{D}$、D和D'相关的格码）在通信领域具有重要应用。本文研究了从q元线性码通过构造D和D'得到的格的一些性质。推导了与构造A的联系、生成矩阵、格体积与最小距离的表达式及界。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。