I would like to thank my advisors Oded Regev and Amnon Ta-Shma for their sage advise and a lot of support during my PhD. I would like to thank them for caring so much and for helping me with everything that I have ever asked for and even more. I would like to thank my lab mates, Avi Ben-Aroya, Iftah Gamzu, Michal Moshkovitz, and Ishay Haviv for many interesting conversations and discussions. I also thank the Israel Science Foundation and the Adams Fellowship Program of the Israel Academy of Sciences and Humanities for its generous financial support. I would like to thank Ely Porat and Omer Reingold, my advisors during my work on Chapter 2. I would also like to thank to Irit Dinur for introducing to me the area of locally decodable codes and for her help during the work on the results in the second chapter

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