Nonexistence of perfect permutation codes under the Kendall τ-metric

被引:0
|
作者
Wang, Xiang [1 ]
Wang, Yuanjie [1 ]
Yin, Wenjuan [2 ]
Fu, Fang-Wei [3 ,4 ]
机构
[1] Coordinat Ctr China CNCERT CC, Natl Comp Network Emergency Response Tech Team, Beijing 100029, Peoples R China
[2] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China
[3] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[4] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
基金
中国国家自然科学基金;
关键词
Flash memory; Permutation codes; Kendall tau-metric; Perfect codes; ERROR-CORRECTION; RANK-MODULATION;
D O I
10.1007/s10623-021-00934-z
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
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, or 5/8(n 2) < 2t + 1 <= (n 2).
引用
收藏
页码:2511 / 2531
页数:21
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