Related papers: Toric Codes from Order Polytopes
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
We report our experiences for the development of a neighborhood algorithm implemented via tree-codes to optimize the performance of a discrete element method (DEM) for convex polytopes. Our implementation of the two-dimensional tree code…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
In this paper, we investigate tropical secant varieties of ordinary linear spaces. These correspond to the log-limit sets of ordinary toric varieties; we show that their interesting parts are combinatorially isomorphic to a certain natural…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
In this paper we study the main characteristics of some evaluation codes parameterized by the edges of a bipartite graph with a perfect matching.
We demonstrate a construction of error-correcting codes from graphs by means of $k$-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the $k$-metric dimension of grid graphs…
A class of counting problems ask for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. We give several efficient algorithms, based on a linear optimization…
This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Toric codes are a class of $m$-dimensional cyclic codes introduced recently by J. Hansen. They may be defined as evaluation codes obtained from monomials corresponding to integer lattice points in an integral convex polytope $P \subseteq…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes. We show that the minimum distance is multiplicative with respect to taking the product of polytopes, and behaves…
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…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…