Outer Strong Blocking Sets

TL;DR

This paper explores the geometry of outer strong blocking sets, introduces their coding theory counterparts, improves bounds on their size, and presents a more efficient construction method.

Contribution

It introduces the concept of outer strong blocking sets, analyzes their structure, and provides a new, computationally efficient construction method.

Findings

Improved upper bound on the size of strong blocking sets

New geometric construction with reduced computational cost

Enhanced understanding of the structure of outer strong blocking sets

Abstract

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.