On Identifying Codes in Binary Hamming Spaces

Identifying and Locating- Dominating Codes in Binary Hamming Spaces Identifying and Locating-Dominating Codes in Binary Hamming Spaces

Acknowledgements First of all I want to thank my supervisor Professor Iiro Honkala for his continuous support, and patience when long breaks in research took place. Many discussions with Iiro, his collaboration, suggestions for research topics, and careful proofreading made this work possible. I also want to thank Dr. Tero Laihonen for many inspiring discussions, suggestions for research topics...

Improved bounds on identifying codes in binary Hamming spaces

On Locating-Dominating Codes in Binary Hamming Spaces

Let F = {0, 1} denote the binary field and F the n-dimensional Cartesian product of it. A code is a subset of F. The elements of F (resp. a code) are called words (resp. codewords) and the Hamming distance d(x, y) between two words x, y ∈ F is the number of coordinate positions in which they differ. The Hamming weight w(x) of a word x ∈ F is the number of 1’s in x. The minimum distance of a cod...

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 ∈ F n, are all nonempty and distinct. A code C ⊆ En is said to be r-d...

Ternary Hamming and binary perfect covering codes

Given 1 1n € Z, the n-cube Q, is the graph with vertex set V : {0, l}' and ed"geset n:VT:orfi, where f' : {(r,w) e V xV: (u _ w)i:1if and only if j: i,(j:0,.'. ,n-l)), for i:0,... ,n-1. The edges of/t aresaidtohave (ortolie along) the directioni,for i 0,.. . ,n-!.Given a graph G, we say that S gVG) is a perfect dom'inating sei (or PDS) of G if every u € V(G) \ S is neighbor of exactly one verte...