On the subset sum problem over finite fields

Authors:
Jiyou Li;Daqing Wan
Affiliations:
School of Mathematical Sciences, Peking University, Beijing 100871, PR China;Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

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.