Let G be the additive group of a finite field. J. Li and D. Wan determined the exact number of solutions of the subset sum problem over G, by giving an explicit formula for the number of subsets of G of prescribed size whose elements sum up to a given element of G. They also determined a closed-form expression for the case where the subsets are required to contain only nonzero elements. In this paper we give an alternative proof of the two formulas. Our argument is purely combinatorial, as in the original proof by Li and Wan, but follows a different and somehow more “natural” approach. We also indicate some new connections with coding theory and combinatorial designs.

令G为有限域的可加群。J. Li 和 D. Wan通过给出指定大小的G的子集数量的明确公式，确定了G 上子集和问题的确切解数，这些子集的元素总和为G的给定元素。对于要求子集仅包含非零元素的情况，他们还确定了一个封闭形式的表达式。在本文中，我们给出了这两个公式的另一种证明。我们的论证纯粹是组合式的，就像 Li 和 Wan 的原始证明一样，但遵循了一种不同的、不知何故更“自然”的方法。我们还指出了与编码理论和组合设计的一些新联系。