Isometries and construction of permutation arrays

Authors:
Mathieu Bogaerts
Affiliations:
Service de Mathématiques, Faculté des Sciences Appliquées, Université Libre de Bruxelles, Bruxelles, Belgium
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

An (n, d)-permutation code is a subset C of Sym(n) such that the Hamming distance dH 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), dH) 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.