Sequences of optimal identifying codes

Locating faulty processors in a multiprocessor system gives the motivation for identifying codes. Denote by l the maximum number of simultaneously malfunctioning processors. We show that if l⩾3, then the problem of finding the smallest cardinality of a (1, ⩽l)-identifying code in a binary hypercube is equivalent to the problem of finding the smallest size of a (2l-1)-fold 1-covering. This observation yields infinite sequences of optimal identifying codes for every l (l⩾3)