Construction Of Error-Correcting Gray Codes Under The L-Infinity-Metric For Rank Modulation

In the rank modulation scheme,Gary codes are very useful in the realization of flash memories.In this scheme,a set of n cells stores information in the permutation induced by the different charge levels of the individual cells.For a gray code in this scheme,two adjacent codewords are obtained by using one "push-to-the-top"operation.Inspired by Yehezkeally,Schwartz and Wang,Fu,we present a construction of error-detecting rank-modulation Gary codes and their popularization on Sn.We study two cases with code length n where n = 3d or n not divided by d([n/d]=2,[n/d]=3)using equivalent transition transformation.