New identifying codes in the binary Hamming space

Irène Charon; Gérard Cohen; Olivier Hudry; Antoine Lobstein

doi:10.1016/j.ejc.2009.03.032

New identifying codes in the binary Hamming space

Irène Charon, Gérard Cohen, Olivier Hudry, Antoine Lobstein

CNRS LTCI

Research output: Contribution to journal › Article › peer-review

Abstract

Let Fⁿ be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r ≥ 1 and x ∈ Fⁿ, we denote by B_r (x) the ball of radius r and centre x. A set C ⊆ Fⁿ is said to be an r-identifying code if the sets B_r (x) ∩ C, x ∈ Fⁿ, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space.

Original language	English
Pages (from-to)	491-501
Number of pages	11
Journal	European Journal of Combinatorics
Volume	31
Issue number	2
DOIs	https://doi.org/10.1016/j.ejc.2009.03.032
Publication status	Published - 1 Feb 2010
Externally published	Yes

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title = "New identifying codes in the binary Hamming space",

abstract = "Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r ≥ 1 and x ∈ Fn, we denote by Br (x) the ball of radius r and centre x. A set C ⊆ Fn is said to be an r-identifying code if the sets Br (x) ∩ C, x ∈ Fn, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space.",

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AU - Charon, Irène

AU - Cohen, Gérard

AU - Hudry, Olivier

AU - Lobstein, Antoine

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Y1 - 2010/2/1

N2 - Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r ≥ 1 and x ∈ Fn, we denote by Br (x) the ball of radius r and centre x. A set C ⊆ Fn is said to be an r-identifying code if the sets Br (x) ∩ C, x ∈ Fn, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space.

AB - Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance. For r ≥ 1 and x ∈ Fn, we denote by Br (x) the ball of radius r and centre x. A set C ⊆ Fn is said to be an r-identifying code if the sets Br (x) ∩ C, x ∈ Fn, are all nonempty and distinct. We give new constructive upper bounds for the minimum cardinalities of r-identifying codes in the Hamming space.

U2 - 10.1016/j.ejc.2009.03.032

DO - 10.1016/j.ejc.2009.03.032

M3 - Article

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EP - 501

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

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ER -

New identifying codes in the binary Hamming space

Abstract

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