Related papers: Partial-MDS Codes and their Application to RAID Ty…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…
In the literature, most of the known high-rate $(n,k)$ MDS array codes with the optimal repair property only support a single repair degree (i.e., the number of helper nodes contacted during a repair process) $d$, where $k\le d\le n-1$.…
Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem:…
Maximum distance separable (MDS) array codes are widely employed in modern distributed storage systems to provide high data reliability with small storage overhead. Compared with the data access latency of the entire file, the data access…
High-rate minimum storage regenerating (MSR) codes are known to require a large sub-packetization level, which can make meta-data management difficult and hinder implementation in practical systems. A few maximum distance separable (MDS)…
Accessing the data in the failed disk (degraded read) with low latency is crucial for an erasure-coded storage system. In this work, the maximum distance separable (MDS) array code with the property of degraded-read friendly (DRF) is…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
A $(k+r,k,l)$ binary array code of length $k+r$, dimension $k$, and sub-packetization $l$ is composed of $l\times(k+r)$ matrices over $\mathbb{F}_2$, with every column of the matrix stored on a separate node in the distributed storage…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes…
MDS self-dual codes have good algebraic structure, and their parameters are completely determined by the code length. In recent years, the construction of MDS Euclidean self-dual codes with new lengths has become an important issue in…
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…
Sum-rank metric codes, as a generalization of Hamming codes and rank metric codes, have important applications in fields such as multi-shot linear network coding, space-time coding and distributed storage systems. The purpose of this study…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search…
Understanding the performance profiles of storage devices and how best to utilize them has always been non-trivial due to factors such as seek times, caching, scheduling, concurrent access, flash wear-out, and garbage collection. However,…
In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed…