2020/11/03 by Xiang, Wang, Yuanjie, Wang, Wenjuan, Yin +1
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2011.01600
In the rank modulation scheme for flash memories, permutation codes have been studied. In this paper, we study perfect permutation codes in Sn, 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 Sn, 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 Sn under the Kendall τ-metric. Further, We prove that there are no perfect t-error-correcting codes in Sn under the Kendall τ-metric for some n and t=2,3,4,or 5.