Related papers: A Generic Transformation to Generate MDS Storage C…
Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time,…
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across…
Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…
In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced…
We give a complete determination of the exact optimal worst-case repair bandwidth and repair I/O for linear exact repair of $(n,n-2,2)$ MDS array codes over every finite field $\mathbb{F}_q$ and for every admissible code length $3\le n\le…
In this paper, we study distributed storage problems over unidirectional ring networks, whose storage nodes form a directed ring and data is transmitted along the same direction. The original data is distributed to store on these nodes.…
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MSR) codes. For both constructions, the encoded symbols are obtained by treating the message vector over GF(q) as a linearized polynomial…
We consider the setting of data storage across n nodes in a distributed manner. A data collector (DC) should be able to reconstruct the entire data by connecting to any k out of the n nodes and downloading all the data stored in them. When…
Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes…
Given the scale of today's distributed storage systems, the failure of an individual node is a common phenomenon. Various metrics have been proposed to measure the efficacy of the repair of a failed node, such as the amount of data download…
This paper studies the design of codes for distributed storage systems (DSS) that enable local repair in the event of node failure. This paper presents locally repairable codes based on low degree multivariate polynomials. Its code…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper,…
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous…
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…