In this paper we settle the question of whether a finite-dimensional vector space \({{\mathcal {V}}}\) over \({\mathbb {F}}_p,\) with p an odd prime, and the family of all the k-sets of elements of \({\mathcal {V}}\) summing up to a given element x, form a 1-\((v,k,\lambda _1)\) or a 2-\((v,k,\lambda _2)\) block design, and, in either case, we find a closed form for \(\lambda _i\) and characterize the automorphism group. The question is discussed also in the case where the elements of the k-sets are required to be all nonzero, as the two cases happen to be intrinsically inseparable. The “twin case” \(p=2,\) which has strict connections with coding theory, was completely discussed in a recent paper by G. Falcone and the present author.

在本文中，我们解决了有限维向量空间\({{\mathcal {V}}}\)是否在\({\mathbb {F}}_p,\)上且p为奇素数的问题，以及\({\mathcal {V}}\)的所有k个元素集合的族，总结为给定元素x，形成 1- \((v,k,\lambda _1)\)或 2- \((v,k,\lambda _2)\)块设计，并且在任何一种情况下，我们都找到了\(\lambda _i\)的封闭形式并刻画了自同构群。在k的元素的情况下也讨论了这个问题-sets 必须全部非零，因为这两种情况恰好在本质上是不可分离的。G. Falcone 和本文作者最近的一篇论文对与编码理论有密切联系的“孪生案例” \(p=2,\)进行了全面讨论。