39 citations · 175 across the 32 of their papers we have counts for
11 papers · 1 filter
The volume polynomial of lattice polygons
Ivan Soprunov, Jenya Soprunova
We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the…
Multigraded Hilbert function and toric complete intersection codes
Mesut Şahin, Ivan Soprunov
Let be a complete -dimensional simplicial toric variety with homogeneous coordinate ring . We study the multigraded Hilbert function of reduced -dimensional subs…
On dual toric complete intersection codes
Pinar Celebi Demirarslan, Ivan Soprunov
In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d-dimensional Newton polytopes, so called toric complete intersection codes. In p…
Toric complete intersection codes
Ivan Soprunov
In this paper we give lower bounds for the minimum distance of evaluation codes constructed from complete intersections in toric varieties. This generalizes the results of Gold-Lit…
Bringing Toric Codes to the next dimension
Ivan Soprunov, Evgenia Soprunova
This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes. We show that the minimum distance is multiplicative w…
Toric surface codes and Minkowski length of polygons
Ivan Soprunov, Evgenia Soprunova
In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), calle…