Moment subset sums over finite fields,Finite Fields and Their Applications

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Moment subset sums over finite fields
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2019-11-18 , DOI: 10.1016/j.ffa.2019.101607
Tim Lai ₁ , Alicia Marino ₂ , Angela Robinson ₃ , Daqing Wan ₄

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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].

中文翻译：

有限域上的矩子集和

有限域上的k子集和问题是一个经典的 NP 完全问题。受编码理论应用的推动，一个更复杂的问题是有限域上的高m矩k子集和问题。我们证明，当评估集是任意次数n的单项式或迪克森多项式的图像集时，对于每个固定m的有限域上的m阶矩k子集和问题，存在确定性多项式时间算法。在经典案例中 $米 = 1$ ，这恢复了 Nguyen-Wang 之前的结果（案例 $米 = 1, p > 2$ ） [22] 以及 Choe-Choe 的结果（案例 $米 = 1, p = 2$ ）[3]。

更新日期：2019-11-18

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