Links between discriminating and identifying codes in the binary hamming space

  • Authors:

  • Irène Charon;Gérard Cohen;Olivier Hudry;Antoine Lobstein

  • Affiliations:

  • GET - Télécom Paris & CNRS, LTCI UMR, Paris Cedex 13, France;GET - Télécom Paris & CNRS, LTCI UMR, Paris Cedex 13, France;GET - Télécom Paris & CNRS, LTCI UMR, Paris Cedex 13, France;GET - Télécom Paris & CNRS, LTCI UMR, Paris Cedex 13, France

  • Venue:
  • AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance, and Ɛn (respectively, On) the set of vectors with even (respectively, odd) weight. For r ≥ 1 and x ∈ Fn, we denote by Br(x) the ball of radius r and centre x. A code C ⊆ Fn is said to be r-identifying if the sets Br(x) ∩ C, x ∈ Fn, are all nonempty and distinct. A code C ⊆ Ɛn is said to be r-discriminating if the sets Br(x) ∩ C, x ∈ On, 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 Fn and the set of r-discriminating codes in Fn+1.