The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Their motivation for identification came from finding malfunctioning processors in multiprocessor systems. Besides that identifying codes can also be applied to sensor networks. In this paper we consider identifying codes in Hamming spaces. We first concentrate on improving the lower bounds on codes which identify words within distance r > 1. These improvements are achieved using a new approach. Then we proceed by introducing new lower bounds on codes identifying sets of words. Constructions for such codes with the best known cardinalities are also given.

In binary Hamming spaces, we construct new 1- identifying codes which improve on previously known upper bounds on the cardinalities of 1-identifying codes for many lengths when n ges 10. We also construct tau-identifying codes using the direct sum of tau codes that are 1-identifying.

In binary Hamming spaces, we construct new$1$-identifying codes from$2$-fold$1$-coverings that are$1$-identifying. We improve on previously known upper bounds for the cardinalities of$1$-identifying codes of many lengths when$n\geq 10$. We construct$t$-identifying codes using the direct sum of$t$$1$-identifying codes. This solves partly an open problem posed by Blass, Honkala, and Litsyn in 2001. We also prove a general result concerning the direct sum of a$t$-identifying code with the whole space of any dimension.

Identifying codes can be used to locate malfunctioning processors. We say that a code C of length n is a linear (1,/spl les/l)-identifying code if it is a subspace of F/sub 2//sup n/ and for all X,Y/spl sube/F/sub 2//sup n/ such that |X|, |Y|/spl les/l and X/spl ne/Y, we have /spl cup//sub x/spl isin/X/(B(x)/spl cap/C)/spl ne//spl cup/y/spl isin/Y(B(y)/spl cap/C). Strongly (1,/spl les/l)-identifying codes are a variant of identifying codes. We determine the cardinalities of optimal linear (1,/spl les/l)-identifying and strongly (1,/spl les/l)-identifying codes in Hamming spaces of any dimension for locating any at most l malfunctioning processors.

A motivation for identifying codes comes from quality control in multiprocessor systems, that is, we are able, with the aid of these codes, to find faulty processors in such a system. We give a construction of two infinite families of optimal codes, which identify up to two malfunctioning processors in Hamming spaces.