2009
DOI: 10.1016/j.jcta.2009.02.004
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On the size of identifying codes in binary hypercubes

Abstract: In this paper, we consider identifying codes in binary Hamming spaces F n , i.e., in binary hypercubes. The concept of (r, )-identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with several possible applications, for example, to sensor networks. Let us denote by M ( ) r (n) the smallest possible cardinality of an (r, )-identifying code in F n . In 2002, Honkala and Lobstein showed for = 1 that lim n→∞ 1 n log 2 M ( ) r (n) = 1 − h(ρ),w… Show more

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Cited by 15 publications
(12 citation statements)
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“…Finding these bounds will help determine best practices for fault detection and design in networked microprocessors. locating-dominating sets have been studied for paths and cycles [8,15,25,26,39,44,70], hypercubes [45,46,47,51,68], and grids [50,66,76]. The mixed-weight OLD-set is also similar to an OLD-set on a directed graph: increased weight can be represented by arcs to other nodes.…”
Section: Discussionmentioning
confidence: 99%
“…Finding these bounds will help determine best practices for fault detection and design in networked microprocessors. locating-dominating sets have been studied for paths and cycles [8,15,25,26,39,44,70], hypercubes [45,46,47,51,68], and grids [50,66,76]. The mixed-weight OLD-set is also similar to an OLD-set on a directed graph: increased weight can be represented by arcs to other nodes.…”
Section: Discussionmentioning
confidence: 99%
“…The mixed-weight open locating-dominating set (mixed-weight OLD-set) models a system in which sensors have varying strengths, represented by placing weights on vertices in the graph. Mixed-weight OLD-sets are related to the weighted or d-identifying code, where all vertices receive the same weight d, which have been studied for paths and cycles [4], hypercubes [12], and other graphs. The mixedweight OLD-set is also similar to an OLD-set on a directed graph: increased weight can be represented by adding arcs to other vertices.…”
Section: Mixed-weight Old-setsmentioning
confidence: 99%
“…If c is an element of Q n and r is a non-negative integer, then B(c, r) denotes the ball of center c and radius r, that is, B(c, r) := {v : v ∈ Q n , d(c, v) ≤ r}. The most recent upper and lower bounds on i (l) r (Q n ) were proved in [5,10,8,9,14]. Adaptive identification in Q n was studied by Junnila [15] who obtained lower and upper bounds on a (1) 1 (Q n ).…”
Section: Introductionmentioning
confidence: 99%