A New Construction of Permutation Arrays

Abstract

Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA p m , p m−1 k for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has |PA(p, k)| • p (m−1)(p−k) m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA p m , p m−1 k for a given index i very simply.