  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 characterisation 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
non-isometric (4,3)- and (5,4)- permutation codes. Maximal and balanced
(n,d)-permutation codes are enumerated in a constructive way.
