Related papers: Characterizations and construction methods for lin…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair…
Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
Locally repairable codes are widely applicable in contemporary large-scale distributed cloud storage systems and various other areas. By making use of some algebraic structures of elliptic curves, Li et al. developed a series of $q$-ary…
In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in…
Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a…
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the…
Distributed storage systems that deploy erasure codes can provide better features such as lower storage overhead and higher data reliability. In this paper, we focus on fractional repetition (FR) codes, which are a class of storage codes…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
Function-correcting codes (FCCs) are designed to provide error protection for the value of a function computed on the data. Existing work typically focuses solely on protecting the function value and not the underlying data. In this work,…
In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The…
Recently, the research on local repair codes is mainly confined to repair the failed nodes within each repair group. But if the extreme cases occur that the entire repair group has failed, the local code stored in the failed group need to…
This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we…
Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional…
Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with $(r,\delta)$-locality that achieve the equality in the Singleton-type…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
We study the performance of Reed-Solomon (RS) codes for the \em exact repair problem \em in distributed storage. Our main result is that, in some parameter regimes, Reed-Solomon codes are optimal regenerating codes, among MDS codes with…
We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…