New identifying codes in the binary Hamming space

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.