Related papers: Explicit and Efficient Constructions of linear Cod…
We consider the task of locally correcting, and locally list-correcting, multivariate linear functions over the domain $\{0,1\}^n$ over arbitrary fields and more generally Abelian groups. Such functions form error-correcting codes of…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…
This paper produces a rate-compatible protograph LDPC code at 1k information blocklength with superior performance in both waterfall and error floor regions. The design of such codes has proved difficult in the past because the constraints…
We introduce randomized Limited View (LV) adversary codes that provide protection against an adversary that uses their partial view of the communication to construct an adversarial error vector to be added to the channel. For a codeword of…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
The insertion-deletion codes were motivated to correct the synchronization errors. In this paper we prove several coordinate-ordering-free upper bounds on the insdel distances of linear codes, which are based on the generalized Hamming…
An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time…
In this paper, we study algebraic geometry codes from curves over $\mathbb{F}_{q^\ell}$ through their virtual projections which are algebraic geometric codes over $\mathbb{F}_q$. We use the virtual projections to provide fractional decoding…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
Locally Decodable Codes (LDCs) are error correcting codes which permit the recovery of any single message symbol with a low number of queries to the codeword (the locality). Traditional LDC tradeoffs between the rate, locality, and error…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
This paper improves the antiGriesmer bound for linear anticodes previously established by Chen and Xie (Journal of Algebra, 673 (2025) 304-320). While the original bound required the code length to satisfy $n < q^{k-1}$ and the dual code to…
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…
Recently introduced Fair-Density Parity-Check (FDPC) codes, targeting high-rate applications, offer superior error-correction performance (ECP) compared to 5G Low-Density Parity-Check (LDPC) codes, given the same number of message-passing…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into…