2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136279The subset sum problem over finite fields is a well-known {\bf 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.16 pagesNumber TheoryInformation Theory11T71;94B35text