In this article, we study locating-dominating codes in binary Hamming spaces \(\mathbb {F}^n\). Locating-dominating codes have been widely studied since their introduction in 1980s by Slater and Rall. They are dominating sets suitable for distinguishing vertices in graphs. Dominating sets as well as locating-dominating codes have been studied in Hamming spaces in multiple articles. Previously, Honkala et al. (Discret Math Theor Comput Sci 6(2):265, 2004) have presented a lower bound for locating-dominating codes in binary Hamming spaces. In this article, we improve the lower bound for all values \(n\ge 10\). In particular, when \(n=11\), we manage to improve the previous lower bound from 309 to 317. This value is very close to the current best known upper bound of 320.

在本文中，我们研究二进制汉明空间\(\mathbb {F}^n\) 中的定位支配代码。自 1980 年代由 Slater 和 Rall 引入以来，定位支配代码已被广泛研究。它们是适用于区分图中顶点的支配集。多篇文章已经在汉明空间中研究了支配集以及定位支配代码。此前，Honkala 等人。(Discret Math Theor Comput Sci 6(2):265, 2004) 提出了二进制汉明空间中定位支配代码的下界。在本文中，我们改进了所有值\(n\ge 10\)的下限。特别地，当\(n=11\)，我们设法将之前的下限从 309 提高到 317。这个值非常接近当前最著名的上限 320。