题 目:Nonexistence of perfect permutation codes under the Kendall -metric
主讲人:王祥
时 间:2022年6月23日,9:00-10:00
地 址:腾讯会议ID:801 388 861
摘 要: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 t-metric. We answer one open problem proposed by Buzaglo and Etzion. That is, proving the nonexistence of perfect codes in Sn, under the Kendall t-metric, for more values of n. Specifically, we present the polynomial representation of the size of a ball in Sn under the Kendall t-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 Sn under the Kendall t-metric for some n and t = 2, 3, 4, 5, or 。
主讲人简介:王祥博士,2017年7月至今就职于国家互联网应急中心,工程师,主要研究方向为编码理论。王祥,2007年9月-2011年6月就读于中南大学获学士学位;2011年9月-2017年6月就读于南开大学陈省身数学研究所获博士学位。在国内外权威学术期刊《Designs, Codes and Crpto.》、《中国科学·信息科学》等上发表论文十余篇。主持国家自然科学青年项目。
邀请人:方伟军
审批人:魏普文