New bounds on binary identifying codes ?
The original motivation for identifying codes comes from fault diagnosis in multiprocessor systems. Currently, the subject forms a topic of its own with several possible applications, for example, to sensor networks. In this paper, we concentrate on identification in binary Hamming spaces. We give a new lower bound on the cardinality of r r -identifying codes when r?2 r ? 2 . Moreover, by a computational method, we show that M1(6)=19 M 1 ( 6 ) = 19 . It is also shown, using a non-constructive approach, that there exist asymptotically good (r,??) ( r , ? ? ) -identifying codes for fixed ??2 ? ? 2 . In order to construct (r,??) ( r , ? ? ) -identifying codes, we prove that a direct sum of r r codes that are (1,??) ( 1 , ? ? ) -identifying is an (r,??) ( r , ? ? ) -identifying code for ??2 ? ? 2 .
identifying code hamming space lower bound direct sum asymptotic behaviour