Related papers: Hierarchical Erasure Correction of Linear Codes
In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical…
Scientific computing workflows generate enormous distributed data that is short-lived, yet critical for job completion time. This class of data is called intermediate data. A common way to achieve high data availability is to replicate…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
Coded computation is a method to mitigate "stragglers" in distributed computing systems through the use of error correction coding that has lately received significant attention. First used in vector-matrix multiplication, the range of…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect…
The piggybacking framework for designing erasure codes for distributed storage has empirically proven to be very useful, and has been used to design codes with desirable properties, such as low repair bandwidth and complexity. However, the…
In this paper we survey the various erasure codes which had been proposed and patented recently, and along the survey we provide introductory tutorial on many of the essential concepts and readings in erasure and Fountain codes. Packet…
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…
We give a method to construct Locally Recoverable Error-Correcting codes. This method is based on the use of rational maps between affine spaces. The recovery of erasures is carried out by Lagrangian interpolation in general and simply by…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that…
We study the largest possible length $B$ of $(B-1)$-dimensional linear codes over $\mathbb{F}_q$ which can correct up to $t$ errors taken from a restricted set $\mathcal{A}\subseteq \mathbb{F}_q^*$. Such codes can be applied to multilevel…
We consider the problem of logical data erasure, contrasting with physical erasure in the same way that end-to-end information flow control contrasts with access control. We present a semantic hierarchy for erasure policies, using a…
The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS)…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
The problem of recovering from qubit erasures has recently gained attention as erasures occur in many physical systems such as photonic systems, trapped ions, superconducting qubits and circuit quantum electrodynamics. While several…