Related papers: List decoding subspace codes from insertions and d…
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
An interpolation-based decoding scheme for interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a probabilistic unique decoder. Both interpretations allow to decode…
In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the distances between the received word…
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…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary…
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…
The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS)…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted…
The interpolation step of Guruswami and Sudan's list decoding of Reed-Solomon codes poses the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…