New identifying codes in the binary Hamming space

Authors:
Irène Charon;Gérard Cohen;Olivier Hudry;Antoine Lobstein
Affiliations:
GET - Télécom Paris & CNRS - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13, France;GET - Télécom Paris & CNRS - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13, France;GET - Télécom Paris & CNRS - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13, France;GET - Télécom Paris & CNRS - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13, France
Venue:
European Journal of Combinatorics
Year:
2010

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Abstract

Let F^n be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r=1 and x@?F^n, we denote by B"r(x) the ball of radius r and centre x. A set C@?F^n is said to be an r-identifying code if the sets B"r(x)@?C, x@?F^n, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space.