论文标题
肯德尔τ-metric下的完美置换代码不存在
Nonexistence of perfect permutation codes under the Kendall τ-metric
论文作者
论文摘要
在闪存记忆的等级调制方案中，已经研究了置换代码。在本文中，我们研究了$ s_n $的完美排列代码，这是Kendallτ-Metric下的$ N $元素上的所有排列。我们回答了Buzaglo和Etzion提出的一个开放问题。也就是说，在Kendallτ-Metric下，以$ n $的价格证明了$ s_n $中完美代码的不存在。具体而言，我们介绍了肯德尔τ-metric下的$ r $ in $ s_n $的球大小的递归公式。此外，我们证明，在Kendall $ N $中，没有完美的$ t $ errector校正代码，其中包括$τ$ - $ n $，$ t $ = 2,3,4或5。
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 τ-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 τ-metric, for more values of $n$. Specifically, we present the recursive formulas for the size of a ball with radius $r$ in $S_n$ under the Kendall τ-metric. Further, We prove that there are no perfect $t$-error-correcting codes in $S_n$ under the Kendall $τ$-metric for some $n$ and $t$=2,3,4,or 5.
