The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this talk we consider codes in the set of all permutations on n elements,
S_n, using the Kendall's tau-metric.
We explore these codes from both theoretical and practical point of view.
In the theoretical side, we prove that there are no perfect single-error-correcting codes in S_n, where n>4 is a prime or 3<n<11.
We also study the concept of diameter perfect codes in S_n.
In the practical side, we study systematic error-correcting codes for permutations.
We present a construction of systematic error-correcting codes in which the number of redundancy symbols is relatively small.