Title :
Isometries and Construction of Permutation Arrays
Author :
Bogaerts, Mathieu
Author_Institution :
Service de Math., Univ. Libre de Bruxelles, Brussels, Belgium
fDate :
7/1/2010 12:00:00 AM
Abstract :
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.
Keywords :
Hamming codes; set theory; Hamming distance; generating algorithms; isometry group; isomorphic objects; maximal-balanced-permutation codes; permutation arrays; permutation code; permutation codes; Character generation; Error correction codes; Hamming distance; Upper bound; Constant composition codes; Hamming distance; isometry; permutation arrays; permutation codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2048449