New bounds on binary identifying codes

Abstract

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 -identifying codes when r ≥ 2 . Moreover, by a computational method, we show that M 1 ( 6 ) = 19 . It is also shown, using a non-constructive approach, that there exist asymptotically good ( r , ≤ ℓ ) -identifying codes for fixed ℓ ≥ 2 . In order to construct ( r , ≤ ℓ ) -identifying codes, we prove that a direct sum of r codes that are ( 1 , ≤ ℓ ) -identifying is an ( r , ≤ ℓ ) -identifying code for ℓ ≥ 2 .