On the size of identifying codes in binary hypercubes

In this paper, we consider identifying codes in binary Hamming spaces Fn, i.e., in binary hypercubes. The concept of (r,??)-identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with several possible applications, for example, to sensor networks.Let us denote by the smallest possible cardinality of an (r,??)-identifying code in Fn. In 2002, Honkala and Lobstein showed for ?=1 that