Small Strong Blocking Sets by Concatenation

TL;DR

This paper introduces explicit constructions of small strong blocking sets in projective spaces using concatenation methods, leading to new minimal codes and saturating sets with sizes linear in dimension.

Contribution

It provides the first explicit infinite families of small strong blocking sets via concatenation, combining geometric and coding theory techniques.

Findings

Constructed infinite families of small strong blocking sets

Achieved sizes linear in the ambient space dimension

Derived small saturating sets as a byproduct

Abstract

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.