相关论文: Some Applications of Coding Theory in Computationa…

Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…

Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman…

This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…

We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…

Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between…

A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…

Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…

Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing…

It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…

High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…

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…

We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…

Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…

Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of…

In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group…

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…

A Locally Recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. We study Locally Recoverable Algebraic Geometry codes arising from…

Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…

We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…