Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide infinite families of small strong blocking sets, whose size is linear in the dimension of the ambient projective spaces. As a byproduct, small saturating sets are obtained.
翻译:坚固的屏蔽装置和它们的对等装置,最低代码,在过去的几年中吸引了人们的极大关注。 将混合的代码构造与对最小性条件的几何洞察结合起来,我们明确提供小型坚固的屏蔽装置的无限家庭,其尺寸在周围投影空间的尺寸是线性的。 作为副产品,我们获得了小的饱和装置。