Moment subset sums over finite fields

Abstract

The k-subset sum problem over finite fields is a classical NP-complete problem. Motivated by coding theory applications, a more complex problem is the higher m-th moment k-subset sum problem over finite fields. We show that there is a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields for each fixed m when the evaluation set is the image set of a monomial or Dickson polynomial of any degree n. In the classical case m=1, this recovers previous results of Nguyen-Wang (the case m=1,p>2) [22] and the results of Choe-Choe (the case m=1,p=2) [3].