In non-adaptive group testing (NAGT), the time for decoding is a crucial problem. Given an unknown string x ∈ {0, 1}N with at most d ones, the problem is how to determine xi = 1 using as few tests as possible so that x can be decoded as fast as possible. A NAGT can be represented by a t ×N matrix. Although we do not know x, this matrix, which is called d-disjunct matrix, can reconstruct it exactly. In this paper, we consider a general problem, in which x is an array of N non-negative integer elements and has up to d positive integers. From nonrandom construction, we prove that we can decode a d-disjunct matrix, which is built from [n, k]q-Reed-Solomon codes and identity matrix Iq, and recover x defined above in poly(d) ·t log2t + O(d3n log(d logN)) with t = O(d2log2N). We also discuss this problem when x contains negative integer elements.Pay-Television internet-based can be applied these results directly. Since the number of customers is very large, our system must be prevented from illegal buyers. This problem is called traitor tracing. To the best of our knowledge, this is the first result that raises a variant of NAGT and gets how to trace traitors without using probability.