New identifying codes in the binary Hamming space

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