Strong blocking sets, introduced first in 2011 in connection with saturating sets, have recently gained a lot of attention due to their correspondence with minimal codes. In this paper, we dig into the geometry of the concatenation method, introducing the concept of outer strong blocking sets and their coding theoretical counterpart. We investigate their structure and provide bounds on their size. As a byproduct, we improve the best-known upper bound on the minimum size of a strong blocking set. Finally, we present a geometric construction of small strong blocking sets, whose computational cost is significantly smaller than the previously known ones.

翻译：强阻塞集最初于2011年与饱和集相关联而提出，近年来因其与最小码的对应关系而受到广泛关注。本文深入探讨了级联方法的几何结构，引入了外强阻塞集的概念及其编码理论对应物。我们研究了外强阻塞集的结构并给出了其大小的界限。作为副产品，我们改进了强阻塞集最小大小的已知最优上界。最后，我们提出了一种小规模强阻塞集的几何构造方法，其计算成本显著低于先前已知的方法。