Related papers: Higher genus universally decodable matrices (UDMG)
Universally decodable matrices (UDMs) can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $N$ and a prime power $q$. The main result of this paper is…
The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of…
Universally decodable matrices can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $n$ and a prime power $q$. Based on Pascal's triangle we give an…
Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices (GDMs) that include EDMs. Each…
We prove a sharp upper bound on the number of distinct columns of a totally unimodular matrix with column sums $1$ improving upon Heller's classical bound. The proof uses Seymour's decomposition theorem. Such matrices are closely related to…
In this paper, we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from covering codes with the covering radius smaller than or equal to $d$. When the list size $L$ is $1$, this gives many new…
Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this paper, we first construct a large family of irreducible representations of the maximal…
An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among…
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…
We extend an earlier result by Dan Abramovich, showing that a conjecture of S. Lang's implies the existence of a uniform bound on the number of $K$-rational points over all smooth curves of genus $g$ defined over $K$, where $K$ is any…
A matrix $H=[d_{ij}]$ is a generalized Hadamard matrix of order $u\lambda$ with entries from $U$ which is a finite group of order $u$ (for short $\mathrm{GH}(u,\,\lambda)$) such that whenever $i\neq \ell$ the set $\{d_{ij}d_{\ell…
Based on work presented in [4], we define $S^2$-Upper Triangular Matrices and $S^2$-Lower Triangular Matrices, two special types of $d\times d(2d-1)$ matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show…
The ranks and kernels of generalized Hadamard matrices are studied. It is proven that any generalized Hadamard matrix $H(q,\lambda)$ over $F_q$, $q>3$, or $q=3$ and $\gcd(3,\lambda)\not =1$, generates a self-orthogonal code. This result…
Generalized diagonal matrices are matrices that have two ladders of entries that are zero in the upper right and bottom left corners. The minors of generic generalized diagonal matrices have square-free initial ideals. We give a description…
As part of the graph minor project, Robertson and Seymour showed in 1990 that the class of graphs that can be embedded in a given surface can be characterized by a finite set of minimal excluded minors. However, their proof, because…
In the present paper we introduce a notion of $G-$decompositions of matrices. Main result of the paper is that a symmetric matrix $A_m$ has a $G-$decomposition in the class of stochastic (resp. substochastic) matrices if and only if $A_m$…
A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any matrix of the form $U = \alpha A + \beta I + \gamma J + \delta D$ with $\alpha \neq 0$, where $I$ is the identity matrix, $J$ is the all-ones matrix and $D$ is the…
We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure $\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the…
A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…
Let $\Mg$ denote the moduli space of compact Riemann surfaces of genus $g$. Mumford had proved that, for each fixed genus $g$, there are isomorphisms asserting that certain higher $DET$ bundles over $\Mg$ are certain fixed…