Codes in permutations and error correction for rank modulation
Arya Mazumdar Alexander Barg
Proceedings of the IEEE International Symposium on Information Theory, Austin, TX, USA, June 2010

Codes  for  rank   modulation  have been recently proposed as a means of protecting flash memory devices from  errors . We study basic  coding  theoretic problems for such  codes , representing them as subsets of the set of  permutations  of  n  elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of  codes . These bounds enable us to establish the exact scaling of the size of optimal  codes  for large values of n. We also show the existence of  codes whose size is within a constant factor of the sphere packing bound for any fixed number of  errors .