On the subset sum problem over finite fields

The subset sum problem over finite fields is a well-known NP-complete problem. It arises naturally from decoding generalized Reed–Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a mathematical point of view. In several interesting cases, we obtain explicit or asymptotic formulas for the solution number. As a consequence, we obtain some results on the decoding problem of Reed–Solomon codes.