Related papers: A characterization of MDS codes that have an error…
Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form $[\mathbf{C} \vert \mathbf{M}]$ where $\mathbf{C}$ is circulant and of column weight $2$, and…
We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So…
We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here,…
Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR)…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance $\delta$ is a family $C$ of graphs on a common vertex set of size $n$, such that if we start with any graph in $C$, we would have to modify…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
Maximum distance separable (MDS) codes are considered optimal because the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are likely the generalized Reed-Solomon (GRS) codes. In 1989, Roth…
Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…
We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be…
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…
Products of MDS codes are of major practical importance; for a recent example, they are used in Data Availability Sampling (DAS) in blockchain networks such as Celestia and as part of the Ethereum roadmap. This motivates us to consider…
Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from…