This thesis discusses matrix properties as they relate to the idea of non-adaptive group testing. This is accomplished by first considering... Show moreThis thesis discusses matrix properties as they relate to the idea of non-adaptive group testing. This is accomplished by first considering the history of group testing and then exploring existing results. The next chapter of this thesis discusses taking a given binary matrix and using this as an inner code with some symbol matrix as an outer code to create a new binary matrix. The process is called a concatenation construction and we will cover a few types including the orthogonal array construction, a 𝜆-separating hash family construction, code concatenation, and DNA Sudoku. We conclude by elaborating on primary results coming from orthogonal array construction and 𝜆-separating hash family constructions. These give results pertaining specifically to Steiner systems and cover-free families. M.S. in Applied Mathematics, May 2015 Show less
