Related papers: State spaces of convolutional codes, codings and e…
A subspace code is a nonempty collection of subspaces of the vector space $\mathbb{F}_q^{n}$. A pair of linear codes is called a linear complementary pair (in short LCP) of codes if their intersection is trivial and the sum of their…
The goal of this paper is to provide a rigorous information-theoretic analysis of subnetworks of interference networks. We prove two coding theorems for the compound multiple-access channel with an arbitrary number of channel states. The…
We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…
The representation, or encoding, utilized in evolutionary algorithms has a substantial effect on their performance. Examination of the suitability of widely used representations for quality diversity optimization (QD) in robotic domains has…
We obtain upper bounds, independent of the ambient dimension, for the number of realizable zero-nonzero patterns and (over ordered fields) sign conditions of a finite family of polynomials $\mathcal P$ restricted to an algebraic subset $V$…
In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…
Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders…
Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be two simple algebras with involution over $K$. In this note we study the embedding problem for algebras with involution. More specifically, if the…
The entanglement properties of a class of topological stabilizer states, the so called \emph{topological color codes} defined on a two-dimensional lattice or \emph{2-colex}, are calculated. The topological entropy is used to measure the…
The invariant theory of finite groups can connect the coding theory to the number theory. In this paper, under this conformity, we obtain the minimal generators of the rings of E-polynomials constructed from the groups related to…
We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of…
The monomial codes over a Galois field F_q that can be thought invariant subspaces are essential to us in this study. More specifically, we look into the link between monomial codes and characteristic subspaces and the decomposition of…
We give a general solution to the question when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
Polygon spaces have been studied extensively, and yet missing from the literature is a simple property that every polygon has: dimension. This is distinct (possibly) from the dimension of the ambient space in which the polygon lives. A…
In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a…