Identifying and Locating- Dominating Codes in Binary Hamming Spaces Identifying and Locating-Dominating Codes in Binary Hamming Spaces
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چکیده
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, and for fruitful collaboration. Professor Aimo Tietäväinen encouraged me to begin my postgraduate studies, and I am grateful for that. I extend my thanks to co-author Professor Geoffrey Exoo, and the reviewers of this thesis, Professor Olivier Hudry and Professor Mark Karpovsky. I am grateful for financial support from Turku Centre for Computer Science (TUCS) and Department of Mathematics. I acknowledge the staff at these institutions for creating pleasant working environment. I acknowledge and thank the Nokia Foundation and the August and Lyydia Heino scholarship fund for partial financial support of my work. Finally, I want to thank my husband Kalle for his loving support and for reading my thesis. The thesis is dedicated to my lovely sons Samuli, Olli, and Vilho, who, throughout this process supplied numerous kisses and hugs.
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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...
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