New bounds on binary identifying codes (Q947104)

\((r,\leq l)\)-identifying codes were introduced by \textit{M. Karpovsky, K. Chakrabarty} and \textit{L. Levitin} [IEEE Trans. Inform. Theory 44, No. 2, 599--611 (1998; Zbl 1105.94342)]. One interesting application of identifying codes is to locate faulty processors in a multiprocessor system. In this article the authors improve known lower bounds on the cardinalities of \((r,\leq 1)\)-identifying codes, combining counting arguments with partial constructions. By using computational methods they also show that the smallest possible cardinality of an \((1,\leq 1)\)-identifying code of length 6 is 18, closing an open question. The last part of the article is focused on constructing \((r,\leq l)\)-identifying codes for \(r\geq 2\) and \(l\geq 2\).