New bounds on binary identifying codes

Authors:
Geoffrey Exoo;Tero Laihonen;Sanna Ranto
Affiliations:
Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA;Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, FIN-20014 Turku, Finland
Venue:
Discrete Applied Mathematics
Year:
2008

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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 M"1(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.