Related papers: Constant dimension codes from Riemann-Roch spaces
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples of the same type, which are locally rigid. In particular,…
A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…
We construct Chern-Simons bundles as $\mathrm{Aut}^{+}P$-equivariant $U(1)$ -bundles with connection over the space of connections $\mathcal{A}_{P}$ on a principal $G$-bundle $P\rightarrow M$. We show that the Chern-Simons bundles are…
We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…
We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and…
We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.
This paper is concerned with the construction of algebraic geometric codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with totally ramified places, which enables us to study…
We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…
A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended…
In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…
We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter,…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
We consider the problem of digitalizing Euclidean line segments from $\mathbb{R}^d$ to $\mathbb{Z}^d$. Christ {\em et al.} (DCG, 2012) showed how to construct a set of {\em consistent digital segment} (CDS) for $d=2$: a collection of…
General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
In this work we investigate unions of lifted MRD codes of a fixed dimension and minimum distance and derive an explicit formula for the cardinality of such codes. This will then imply a lower bound on the cardinality of constant dimension…