In the rank modulation scheme for flash memories, permutation codes have been studied. In this paper, we study perfect permutation codes in \(S_n\), the set of all permutations on n elements, under the Kendall \(\tau \)-metric. We answer one open problem proposed by Buzaglo and Etzion. That is, proving the nonexistence of perfect codes in \(S_n\), under the Kendall \(\tau \)-metric, for more values of n. Specifically, we present the polynomial representation of the size of a ball in \(S_n\) under the Kendall \(\tau \)-metric for some radius r, and obtain some sufficient conditions of the nonexistence of perfect permutation codes. Further, we prove that there does not exist a perfect t-error-correcting code in \(S_n\) under the Kendall \(\tau \)-metric for some n and \(t=2,3,4,5,~\text {or}~\frac{5}{8}\left( {\begin{array}{c}n\\ 2\end{array}}\right) < 2t+1\le \left( {\begin{array}{c}n\\ 2\end{array}}\right) \).

在闪存的秩调制方案中，已经研究了置换码。在本文中，我们在 Kendall \(\tau \)度量下研究\(S_n\) 中的完美排列代码，这是n 个元素上所有排列的集合。我们回答了 Buzaglo 和 Etzion 提出的一个开放性问题。也就是说，证明在\(S_n\) 中不存在完美代码，在 Kendall \(\tau \)度量下，对于更多的n值。具体来说，我们在 Kendall \(\tau \) -metric下给出了球在\(S_n\)中的大小的多项式表示，对于某些半径r，并得到完美置换码不存在的一些充分条件。此外，我们证明了不存在一个完美的吨在-error校正码\（S_N \）肯德尔下\（\ tau蛋白\） -metric一些Ñ和\（T = 2,3,4,5， ~\text {or}~\frac{5}{8}\left( {\begin{array}{c}n\\ 2\end{array}}\right) < 2t+1\le \left( { \begin{array}{c}n\\ 2\end{array}}\right) \)。