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Setting Limits on Supersymmetry Using Simplified Models
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Moment subset sums over finite fields.

Tim Lai1, Alicia Marino2, Angela Robinson3

  • 1Indiana University, Bloomington.

Finite Fields and Their Applications
|March 18, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields. This advancement is significant for coding theory applications, offering efficient solutions for complex computational problems.

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Area of Science:

  • Computational Complexity
  • Finite Field Theory
  • Coding Theory

Background:

  • The k-subset sum problem is a known NP-complete problem.
  • The m-th moment k-subset sum problem is a more complex variant with applications in coding theory.

Purpose of the Study:

  • To develop a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields.
  • To extend existing results for the classical k-subset sum problem.

Main Methods:

  • Development of a deterministic polynomial time algorithm.
  • Analysis of the m-th moment k-subset sum problem over finite fields.
  • Consideration of evaluation sets derived from monomial or Dickson polynomials.

Main Results:

  • A deterministic polynomial time algorithm is presented for the m-th moment k-subset sum problem for any fixed m.
  • The algorithm is effective when the evaluation set is the image set of a monomial or Dickson polynomial.
  • This work generalizes and recovers previous results for the classical m=1 case.

Conclusions:

  • The proposed algorithm provides an efficient solution for a complex problem in computational complexity and coding theory.
  • The findings have implications for advancing research in finite field algorithms and their applications.