标题： 通过构造D、D$^{'}$和$\overline{D}$得到的$q$-元格点的$l_1$-距离的界 显示英文标题

标题： Bounds for the $l_1$-distance of $q$-ary lattices obtained via Constructions D, D$^{'}$ and $\overline{D}$

摘要： 格已被用于编码理论和密码学中的几个问题。 在本文中，我们研究了通过 构造 D，$\D'$和$\overline{D}$获得的$q$-元格。 展示了构造 D 与$\D'$之间的联系。 格的最小$l_1$-距离的界 $\Lambda_{D}$, $\Lambda_{D'}$ 和 $\Lambda_{\overline{D}}$ 以及在某些条件下，$\Lambda_{D'}$的生成矩阵被提出。 此外，当所使用的码链在零一加法下封闭时，我们推导出与这些构造中所用码的距离相关的格子$\Lambda_{D}$和$\Lambda_{\overline{D}}$的最小$l_1$-距离的显式表达式。 显示英文摘要

摘要： Lattices have been used in several problems in coding theory and cryptography. In this paper we approach $q$-ary lattices obtained via Constructions D, $\D'$ and $\overline{D}$. It is shown connections between Constructions D and $\D'$. Bounds for the minimum $l_1$-distance of lattices $\Lambda_{D}$, $\Lambda_{D'}$ and $\Lambda_{\overline{D}}$ and, under certain conditions, a generator matrix for $\Lambda_{D'}$ are presented. In addition, when the chain of codes used is closed under the zero-one addition, we derive explicit expressions for the minimum $l_1$-distances of the lattices $\Lambda_{D}$ and $\Lambda_{\overline{D}}$ attached to the distances of the codes used in these constructions.