在一定维数上不存在完美$2$ -纠错Lee码
Nonexistence of perfect $2$-error-correcting Lee codes in certain dimensions
摘要：
Golomb-Welch猜想指出，对于$n \ge 3$和$e \ge 2$，在$\mathbb{Z}^n$中不存在完美的$e$ -纠错码。本文证明了对于一类期望为无穷大的$n$，不存在完美$2$ -纠错码.这一结果进一步证实了Golomb-Welch猜想。
英文摘要：
The Golomb--Welch conjecture states that there are no perfect $e$-error-correcting codes in $\mathbb{Z}^n$ for $n \ge 3$ and $e \ge 2$. In this note, we prove the nonexistence of perfect $2$-error-correcting codes for a certain class of $n$, which is expected to be infinite. This result further substantiates the Golomb--Welch conjecture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
