Related papers: Cyclic Codes with Locality and Availability
Locally repairable codes have been investigated extensively in recent years due to practical application in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has…
In this article, we construct codes with hierarchical locality using natural geometric structures in Artin-Schreier surfaces of the form $y^p-y=f(x,z)$. Our main theorem describes the codes, their hierarchical structure and recovery…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
For any prime $p$, $\lambda$-constacyclic codes of length $p^s$ over ${\cal R}=\mathbb{F}_{p^m} + u\mathbb{F}_{p^m}$ are precisely the ideals of the local ring ${\cal R}_{\lambda}=\frac{{\cal R}[x]}{\left\langle x^{p^s}-\lambda…
The (n, k, r)-Locally recoverable codes (LRC) studied in this work are (n, k) linear codes for which the value of each coordinate can be recovered by a linear combination of at most r other coordinates. In this paper, we are interested to…
Locally recoverable codes (LRCs) with locality parameter $r$ can recover any erased code symbol by accessing $r$ other code symbols. This local recovery property is of great interest in large-scale distributed classical data storage systems…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is…
Let $R=\mathbb{Z}_q+u\mathbb{Z}_q$, where $q=p^s$ and $u^2=0$. In this paper, some structural properties of cyclic codes over the ring $R$ are considered. A necessary and sufficient condition for cyclic codes over the ring $R$ to be free is…
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
In a recent work, quantum locally recoverable codes (qLRCs) have been introduced for their potential application in large-scale quantum data storage and implication for quantum LDPC codes. This work focuses on the bounds and constructions…
A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and…
We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…