New identifying codes in the binary Hamming space

AbstractLet Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r≥1 and x∈Fn, we denote by Br(x) the ball of radius r and centre x. A set C⊆Fn is said to be an r-identifying code if the sets Br(x)∩C, x∈Fn, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space