DISJUNCTNESS PROPERTIES RESULTING FROM CONCATENATION OF GROUP TESTING MATRICES Clardy, Melinda Bulin This 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 Ellis, Robert 2015 2015-05 Thesis application/pdf islandora:8021 http://hdl.handle.net/10560/3502 MATH / Applied Mathematics Illinois Institute of Technology en In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access