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：多级格码（诸如与构造$C$、$\overline{D}$、D和D'相关的格码）在通信领域具有重要应用。本文研究了基于$q$元线性码通过构造D与D'所获取格的一些性质。推导了其与构造A的关联、生成矩阵、格体积与最小距离的表达式及界。此外，还给出了对二进制及$p$元线性码（$p$为素数）的构造与解码相关先前结果的扩展。