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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

18 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	491-501
Nombre de pages	11
journal	European Journal of Combinatorics
Volume	31
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.ejc.2009.03.032
état	Publié - 1 févr. 2010
Modification externe	Oui

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10.1016/j.ejc.2009.03.032

Contient cette citation

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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 - Cohen, Gérard

AU - Hudry, Olivier

AU - Lobstein, Antoine

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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.

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New identifying codes in the binary Hamming space

Résumé

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