Related papers: Isometry and Automorphisms of Constant Dimension C…
In this paper we will discuss isometries and strong isometries for convolutional codes. Isometries are weight-preserving module isomorphisms whereas strong isometries are, in addition, degree-preserving. Special cases of these maps are…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and…
An (n,d)-permutation code is a subset C of Sym(n) such that the Hamming distance d_H between any two distinct elements of C is at least equal to d. In this paper, we use the characterisation of the isometry group of the metric space…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…
Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this…
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
We study the automorphisms of binary stabilizer codes and states. We prove that they almost always form a solvable group, and thereby shed new light on the fact that there is no universal set of transversal gates. We also determine the…
We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in…
In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all…
We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of the asymptotic dimension with the asymptotic inductive…
With each piecewise monotonic map of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…