Article ID Journal Published Year Pages File Type
420586 Discrete Applied Mathematics 2008 14 Pages PDF
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 rr-identifying codes when r≥2r≥2. Moreover, by a computational method, we show that M1(6)=19M1(6)=19. It is also shown, using a non-constructive approach, that there exist asymptotically good (r,≤ℓ)(r,≤ℓ)-identifying codes for fixed ℓ≥2ℓ≥2. In order to construct (r,≤ℓ)(r,≤ℓ)-identifying codes, we prove that a direct sum of rr codes that are (1,≤ℓ)(1,≤ℓ)-identifying is an (r,≤ℓ)(r,≤ℓ)-identifying code for ℓ≥2ℓ≥2.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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