Links Between Discriminating and Identifying Codes in the Binary Hamming Space

Let Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hamming distance, and En (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 ⊆ En 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 F n+1 . 1 hal-00477681,version1-29Apr2010 Author manuscript, published in "Applicable Algebra in Engineering, Communication and Computing, Bangalore : India (2007)" 

• Type: Conference
• Year: 2007
• Where: AAECC
• Authors: Irène Charon, Gérard D. Cohen, Olivier Hudry, Antoine Lobstein
• Keywords: AAECC 2007, Algorithms, Binary Hamming Space, Hamming Distance, Hamming Space