Related papers: Regev's reduction as a candidate quantum algorithm…
Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
Today's massively-sized datasets have made it necessary to often perform computations on them in a distributed manner. In principle, a computational task is divided into subtasks which are distributed over a cluster operated by a…
Motivated by applications in storage systems and property testing, we study data stream algorithms for local testing and tolerant testing of codes. Ideally, we would like to know whether there exist asymptotically good codes that can be…
In the rank-constrained optimization problem (RCOP), it minimizes a linear objective function over a prespecified closed rank-constrained domain set and $m$ generic two-sided linear matrix inequalities. Motivated by the Dantzig-Wolfe (DW)…
We present a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for the production of a pair of leptons in Drell-Yan process and of Higgs boson in gluon fusion as well as in bottom quark…
We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
In this paper show that the list and bounded-distance decoding problems of certain bounds for the Reed-Solomon code are at least as hard as the discrete logarithm problem over finite fields.
Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Quantum computing represents a significant advancement in computational capabilities. Of particular concern is its impact on asymmetric cryptography through, notably, Shor's algorithm and the more recently developed Regev's algorithm for…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
We consider a list decoding algorithm recently proposed by Pellikaan-Wu \cite{PW2005} for $q$-ary Reed-Muller codes $\mathcal{RM}_q(\ell, m, n)$ of length $n \leq q^m$ when $\ell \leq q$. A simple and easily accessible correctness proof is…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…