Anurag Bishnoi (TU Delft): Blocking sets and minimal codes from expander graphs

Véges Geometria szeminárium

Abstract:

Finite geometry has played an important role in giving constructions of various interesting families of graphs. In this talk, I will show that the other direction can be equally fruitful. By using explicit constant-degree expanders, and asymptotically good codes, we give an explicit construction of optimal (up-to a constant factor) strong blocking sets in finite projective spaces. Our construction resolves one of the main open problems on minimal codes, as these codes have been shown to be equivalent to strong blocking sets. It also gives new explicit constructions of affine blocking sets and trifferent codes.