  We consider identifying codes in binary Hamming spaces F^n, i.e., in binary
hypercubes. The concept of 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 C be a subset of F^n. For any subset X of F^n, denote by I_r(X)=I_r(C;X)
the set of elements of C within distance r from at least one x in X. Now C is
called an (r,<= l)-identifying code if the sets I_r(X) are distinct for all
subsets X of size at most l. We estimate the smallest size of such codes with
fixed l and r/n converging to some number rho in (0,1). We further show the
existence of such a code of size O(n^{3/2}) for every fixed l and r slightly
less than n/2, and give for l=2 an explicit construction of small such codes
for r the integer part of n/2-1 (the largest possible value).
