Related papers: Error-Correction of Multidimensional Bursts
Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with higher error threshold and high tolerating loss rates. We present a topological a error…
In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions…
We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…
Folding a sequence $S$ into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes. The new…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
In order to build a scalable quantum computer error correction will be required to reduce the impact of errors. Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault…
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
Error correcting codes are defined and important parameters for a code are explained. Parameters of new codes constructed on algebraic surfaces are studied. In particular, codes resulting from blowing up points in $\proj^2$ are briefly…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
In fiber-fed galaxy redshift surveys, the finite size of the fiber plugs prevents two fibers from being placed too close to one another, limiting the ability of studying galaxy clustering on all scales. We present a new method for…
An error model with asymmetric single magnitude four error is considered. This paper is about constructions of codes correcting single error over $\mathbb{Z}_{2^{a}3^{b}r}$. Firstly, we reduce the construction of a maximal size…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…