39 citations · 175 across the 32 of their papers we have counts for
5 papers · 1 filter
An algebraic-combinatorial proof of a Bezout-type inequality for mixed volumes of three-dimensional zonoids
Gennadiy Averkov, Ivan Soprunov
We present a new algebraic-combinatorial approach to proving a Bezout-type inequality for zonoids in dimension three, which has recently been established by Fradelizi, Madiman, Mey…
Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respec…
On the affine permutation group of certain decreasing Cartesian codes
Eduardo Camps-Moreno, Hiram H. López, Eliseo Sarmiento +1
A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (s…
Mixed volumes of zonoids and the absolute value of the Grassmannian
Gennadiy Averkov, Katherina von Dichter, Simon Richard +1
Zonoids are Hausdorff limits of zonotopes, while zonotopes are convex polytopes defined as the Minkowski sums of finitely many segments. We present a combinatorial framework that l…
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…