Some Constructions About Disjunct Matrix

Firstly, we construct some disjunct matrices on complete graph and affine space (Theorem 2.1.1 - Theorem 3.2), the results have good disjunct property . Next, we construct a matrixM_r (â–³) on simplicial complex , and gain a new matrix M_r(â–³) as that which results by row augmenting the matrix M_r(â–³) with M₁^c(â–³)(Theorem 4.2). We prove that it is a disjunct matrix, and when 1≤r < t < k, we compute the Hamming distance of any two unions of at mostr columns in M_r(â–³), and prove that M_r(â–³) could correct an error; when 2≤r < t < k,we compute the Hamming distance of any two unions of at most r - 1 columns in M_r(â–³),and prove that M_r(â–³) could correct two errors. Finally, we use block design to construct a d^e disjunct matrix(Theorem 5.1), it could correct and detect errors in the test result.