Related papers: Multilayer crisscross error and erasure correction
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
In this paper we study properties and invariants of matrix codes endowed with the rank metric, and relate them to the covering radius. We introduce new tools for the analysis of rank-metric codes, such as puncturing and shortening…
The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…
Constant dimension codes (CDCs) are essential for error correction in random network coding. A fundamental problem of CDCs is to determine their maximal possible size for given parameters. Inserting construction and multilevel construction…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has…
This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the…
We define the Euclidean hull of a linear code $C$ as the intersection of $C$ and its Euclidean dual $C^\perp$. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing…
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…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
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 square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of such systems within the classical coding theory. We show how we…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
Rank metric codes and constant-dimension codes (CDCs) have been considered for error control in random network coding. Since decoder errors are more detrimental to system performance than decoder failures, in this paper we investigate the…
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
In their 2007 book, Tsfasman and Vl\v{a}du\c{t} invite the reader to reinterpret existing coding theory results through the lens of projective systems. Redefining linear codes as projective systems provides a geometric vantage point. In…
We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$…