Permutation Arrays Under the Chebyshev Distance

Abstract

An (n, d) permutation array (PA) is a subset of S(n) with the property that the distance (under some metric) between any two permutations in the array is at least d. 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.