Zobrazeno 1 - 10
of 91
pro vyhledávání: '"Soprunov, Ivan"'
Autor:
Averkov, Gennadiy, Soprunov, Ivan
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, Meyer, and Zvavitch. Our approach hints at connections between inequaliti
Externí odkaz:
http://arxiv.org/abs/2409.18928
Autor:
Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
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 respect to the CSS-T poset, and we also study how to derive new triorthogona
Externí odkaz:
http://arxiv.org/abs/2408.02916
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 (some) toric codes. The affine permutations consist of the permutations
Externí odkaz:
http://arxiv.org/abs/2405.08112
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 links the study of mixed volumes of zonoids (a topic that has applicati
Externí odkaz:
http://arxiv.org/abs/2404.02842
Autor:
Soprunov, Ivan, Soprunova, Jenya
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 Heine-Shephard problem for two bodies in the plane. As an application
Externí odkaz:
http://arxiv.org/abs/2401.06111
Autor:
Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
Publikováno v:
Quantum Inf Process 23, 230 (2024)
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and the shorteni
Externí odkaz:
http://arxiv.org/abs/2312.17518
Autor:
Anderson, Sarah E., Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, Soprunov, Ivan
Given two $q$-ary codes $C_1$ and $C_2$, the relative hull of $C_1$ with respect to $C_2$ is the intersection $C_1\cap C_2^\perp$. We prove that when $q>2$, the relative hull dimension can be repeatedly reduced by one, down to a certain bound, by rep
Externí odkaz:
http://arxiv.org/abs/2212.14521
Autor:
Averkov, Gennadiy, Soprunov, Ivan
Any collection of $n$ compact convex planar sets $K_1,\dots, K_n$ defines a vector of ${n\choose 2}$ mixed areas $V(K_i,K_j)$ for $1\leq i
Externí odkaz:
http://arxiv.org/abs/2112.13128
For a given lattice polytope $P$ in $\mathbb{R}^3$, consider the space $\mathcal{L}_P$ of trivariate polynomials over a finite field $\mathbb{F}_q$, whose Newton polytopes are contained in $P$. We give an upper bound for the maximum number of $\mathb
Externí odkaz:
http://arxiv.org/abs/2105.10071
Publikováno v:
Designs, Codes and Cryptography, 89 (2021), no. 7, 1367-1403
The aim of this work is to study the dual and the algebraic dual of an evaluation code using standard monomials and indicator functions. We show that the dual of an evaluation code is the evaluation code of the algebraic dual. We develop an algorithm
Externí odkaz:
http://arxiv.org/abs/2012.10016