Ivan Soprunov

Toric Surface Codes and Minkowski Length of Polygons

In this paper we prove new lower bounds for the minimum distance of a toric surface code

Bringing Toric Codes to the Next Dimension

\mathcal{C}_P

Toric complete intersection codes

defined by a convex lattice polygon

Bezout Inequality for Mixed Volumes

P\subset\mathbb{R}^2

Multigraded Hilbert Functions and Toric Complete Intersection Codes

. The bounds involve a geometric invariant

Characterization of Simplices via the Bezout Inequality for Mixed Volumes

L(P)

Eventual quasi-linearity of the Minkowski length

, called the full Minkowski length of

Lattice polytopes in coding theory

P

Generalized multiplicities of edge ideals

. We also show how to compute

Tropical determinant on transportation polytopes

L(P)