Related papers: Constant dimension codes from Riemann-Roch spaces
In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of…
Constant dimension codes (CDCs) are essential for error correction in random network coding. A fundamental problem of CDCs is to determine their maximal possible size for given parameters. Inserting construction and multilevel construction…
The linkage construction and its generalization is one of the most powerful constructions for constant dimension code, accounting for approximately 50\% of all the listed parameters. We show how to improve the linkage construction of…
Let C be a projective curve defined over a field k and let D be a divisor of C. The Riemann-Roch space L(D) is the set of rational functions on C for which certain zeros are imposed and certain poles are allowed, with some multiplicities…
Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Using skew polynomials $f\in R$, we construct division algebras and a generalization of maximum rank distance codes…
Cone spherical metrics, defined on compact Riemann surfaces, are conformal metrics with constant curvature one and finitely many cone singularities. Such a metric is termed \textit{reducible} if a developing map of the metric has monodromy…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
Given a smooth curve X of genus g we compute de dimension of the family of curves C which have an involution over X. Moreover we distinguish when the curve C is hyperelliptic.
We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.
Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…
On a basis of theory of Riemann extension of the space of constant affine connection associated with the R\"ossler system of equations relations between its parameters are investigated.
We apply the theory of Peres and Schlag to obtain estimates for generic Hausdorff dimension distortion under orthogonal projections on simply connected two dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain…
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 natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor contruction of Mumford from sheaves to…
We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…
A description of complete normal varieties with lower dimensional torus action has been given by Altmann, Hausen, and Suess, generalizing the theory of toric varieties. Considering the case where the acting torus T has codimension one, we…
The almost sure value of the Hausdorff dimension of limsup sets generated by randomly distributed rectangles in the Heisenberg group is computed in terms of directed singular value functions.
For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one point divisors, and…
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental…
This paper contains a comparative study of two families of simple curves drawn in the plane. On the one hand, we have the fractal curves on the unit interval, with self-similar structure, which have associated a Hausdorff dimension. On the…