New bounds on binary identifying codes |
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Authors: | Geoffrey Exoo |
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Institution: | a Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA b Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, FIN-20014 Turku, Finland |
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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 M1(6)=19. It is also shown, using a non-constructive approach, that there exist asymptotically good (r,≤?)-identifying codes for fixed ?≥2. In order to construct (r,≤?)-identifying codes, we prove that a direct sum of r codes that are (1,≤?)-identifying is an (r,≤?)-identifying code for ?≥2. |
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Keywords: | Identifying code Hamming space Lower bound Asymptotic behaviour Direct sum |
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