Related papers: Decoding Algebraic Geometry codes by a key equatio…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
We investigate multi-point algebraic geometric codes defined from curves related to the generalized Hermitian curve introduced by Alp Bassa, Peter Beelen, Arnaldo Garcia, and Henning Stichtenoth. Our main result is to find a basis of the…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
We present an algorithm (CoDeFi) which overcomes the curse of dimensionality (CoD) in scientific computations and, especially, in mathematical finance (Fi). Our method applies a broad class of partial differential equations such as…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
A characterization of the symmetry algebra of the $n$th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method…
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A…
In this article, we present a new construction of codes from algebraic curves. Given a curve over a non-prime finite field, the obtained codes are defined over a subfield. We call them Cartier Codes since their construction involves the…
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using any further information about the integrand) are added to the…
This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on…