We propose new combinatorial constructions of partitions into perfect codes in both the Hamming and Lee metrics. Also, we present a new combinatorial construction method for diameter perfect codes in the Lee metric, which is further developed to a construction of partitions into such codes. For the Lee metric, we improve previously known lower bounds on the number of perfect and diameter perfect codes proposed by Etzion in 2011.

中文翻译：

---

Hamming 和 Lee 度量中的完美代码分区

我们在 Hamming 和 Lee 度量中提出了将分区的新组合构造成完美代码。此外，我们提出了一种新的 Lee 度量中直径完美码的组合构造方法，该方法进一步发展为将分区构造为此类码。对于 Lee 度量，我们改进了先前已知的 Etzion 在 2011 年提出的完美和直径完美代码数量的下限。