Rewrite Cost optimal Rank Modulation Codes in S4 and S5

In this paper, we have found all possible largest permutation codes in S
₄
and S
₅
under Kendall T-distance. We consider two rewrite operations namely push-to-the-top and minimal-push-up and give the optimum codes in terms of rewrite cost for both these techniques. These optimum codes can be obtained from a set of relatively smaller size for both the cases. We also give the largest single error correcting Gray code when minimal-push-up is used.