The Construction of Disjunct Matrix for Non-Adaptive Group Testing

Historically, group testing theory related to the testing of blood samples to identify a disease. Based on the algorithm, there are two types of group testing, Adaptive Group Testing (AGT) and Non-Adaptive Group Testing (NAGT). NAGT algorithm can be represented by a binary matrix M = m_ij, where columns are labeled by items and rows by tests (blocks). Criteria of matrix is m _ij = 1 if test i contains item j and the other m _ij = 0. On the other hand, the test results of each block are represented by a column vector, called outcome vector. Based on these representations, the problem of group testing can be viewed as finding representation matrix M which satisfies the equation Mx = y, where y is an outcome vector and x are tested samples. If there are d positive samples of n samples then we say d-Combinatorial Group Testing, abbreviated by d-CGT. This paper presents two constructions of disjunct matrix. The first construction based on generating of binary matrices and the second construction using modular equation. Furthermore, from the construction will be modified such that the new construction can be identified more than d positive samples.