Isometries and Construction of Permutation Arrays

An (n,d)-permutation code is a subset C of Sym(n) such that the Hamming distance d_H between any two distinct elements of C is at least equal to d . In this paper, we use the characterization of the isometry group of the metric space (Sym(n),d_H) in order to develop generating algorithms with rejection of isomorphic objects. To classify the (n,d) -permutation codes up to isometry, we construct invariants and study their efficiency. We give the numbers of nonisometric (4, 3) - and (5, 4)- permutation codes. Maximal and balanced (n,d)-permutation codes are enumerated in a constructive way.