%0 Journal Article
%T Isometries and Construction of Permutation Arrays
%A Mathieu Bogaerts
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0911.1713v1