An(n,d) permutation array (PA) is a subset ofSnwith the property that the distance (under some metric) between any two permutations in the array is at leastd. They became popular recently for communication over power lines. Motivated by an application to flash memories, in this paper, the metric used is the Chebyshev metric. A number of different constructions are given, as well as bounds on the size of such PA.

An (n, d) permutation array (PA) is a subset of Snwith the property that the distance (under any distance metric, such as Hamming) between any two permutations in the array is at least d, which becomes popular recently for communication over power line. We use l∞-norm to measure the distance between permutations, and give a construction of permutation arrays under l∞-norm together with efficient encoding and decoding algorithms. This construction is the first of its kind.

We give a simple construction of distance-preserving mappings from ternary vectors to permutations (3-DPM). Our result gives a lower bound for permutation arrays, i.e., P(n, d) ges A3(n, d) , which significantly improves previous lower bounds for d les 3n / 5.