We solve several first questions in the table of small parameters of completely regular (CR) codes in Hamming graphs $H(n,q)$. The most uplifting result is the existence of a $\{13,6,1;1,6,9\}$-CR code in $H(n,2)$, $n\ge 13$. We also establish the non-existence of a $\{11,4;3,6\}$-code and a $\{10,3;4,7\}$-code in $H(12,2)$ and $H(13,2)$. A partition of the complement of the quaternary Hamming code of length~$5$ into $4$-cliques is found, which can be used to construct completely regular codes with covering radius $1$ by known constructions. Additionally we discuss the parameters $\{24,21,10;1,4,12\}$ of a putative completely regular code in $H(24,2)$ and show the nonexistence of such a code in $H(8,4)$. Keywords: Hamming graph, equitable partition, completely regular code

翻译：我们解决了 Hamming 图 $H(n,q)$ 中完全正则 (CR) 码的小参数表中的若干首要问题。最令人振奋的结果是存在一个 $\{13,6,1;1,6,9\}$-CR 码于 $H(n,2)$ 中，其中 $n\ge 13$。我们还确定了在 $H(12,2)$ 和 $H(13,2)$ 中不存在 $\{11,4;3,6\}$-码以及 $\{10,3;4,7\}$-码。我们找到了将长度为~$5$ 的四元 Hamming 码的补集划分为 $4$-团的方法，这可用于通过已知构造方法构造覆盖半径为 $1$ 的完全正则码。此外，我们讨论了 $H(24,2)$ 中一个假定完全正则码的参数 $\{24,21,10;1,4,12\}$，并证明了在 $H(8,4)$ 中不存在这样的码。关键词：Hamming 图，公平划分，完全正则码