Finite Geometry,

Algebraic Combinatorics

& Coding Theory

e-seminars

FGAC²T is an online seminar series dedicated to people working in the area of Finite Geometry, Algebraic Combinatorics and Coding Theory. The purpose is to spread scientific contributions in this area of Mathematics and to engage in discussions with participants even geographically distant from each other.

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22nd July 2025

14:00 CEST (UTC+2 )

Anurag Bishnoi
(Delft University of Technology)

Using expander graphs to construct strong blocking sets and minimal codes
(joint work(s) with Noga Alon, Shagnik Das, Alessandro Neri, and István Tomon)

Abstract:

In this talk, we will present the recent graph-theoretic method of constructing strong blocking sets and their generalizations. A strong blocking set is a set of points that meets every hyperplane in a spanning set of the hyperplane. These objects are known to be equivalent to linear minimal codes. We will also show a connection between these and affine blocking sets for codimension 2 subspaces. We obtain an asymptotically optimal explicit construction using constant degree expanders. Moreover, we will present the asymptotically optimal construction of strong s-blocking sets for s > 1 using hypergraphs.