Links Between Discriminating and Identifying Codes in the Binary Hamming Space

  • Irène Charon
  • Gérard Cohen
  • Olivier Hudry
  • Antoine Lobstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


Let F n be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance, and \({\cal E}^n\) (respectively, \({\cal O}^n\)) the set of vectors with even (respectively, odd) weight. For r ≥ 1 and x ∈ F n , we denote by B r (x) the ball of radius r and centre x. A code C ⊆ F n is said to be r-identifying if the sets B r (x) ∩ C, x ∈ F n , are all nonempty and distinct. A code \(C\subseteq {\cal E}^n\) is said to be r-discriminating if the sets B r (x) ∩ C, \(x\in {\cal O}^n\), are all nonempty and distinct. We show that the two definitions, which were given for general graphs,are equivalent in the case of the Hamming space, in the following sense: for any odd r, there is a bijection between the set of r-identifying codes in F n and the set of r-discriminating codes in F n + 1.


Graph Theory Coding Theory Discriminating Codes Identifying Codes Hamming Space Hypercub 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Irène Charon
    • 1
  • Gérard Cohen
    • 1
  • Olivier Hudry
    • 1
  • Antoine Lobstein
    • 1
  1. 1.GET - Télécom Paris & CNRS - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13France

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