Related papers: A Fast Decoding Algorithm for Generalized Reed-Sol…
This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over $\mathbb{F}_{q^m}$ whose entries lie in a fixed collection of…
We study the list-decoding problem of alternant codes, with the notable case of classical Goppa codes. The major consideration here is to take into account the size of the alphabet, which shows great influence on the list-decoding radius.…
The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the…
A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from…
The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but…
Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated…
Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments,…
In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and…
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
In this paper we present a modification of Reed-Solomon codes that beats the Guruwami-Sudan $1-\sqrt{R}$ decoding radius of Reed-Solomon codes at low rates $R$. The idea is to choose Reed-Solomon codes $U$ and $V$ with appropriate rates in…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
We show how to solve a generalised version of the Multi-sequence Linear Feedback Shift-Register (MLFSR) problem using minimisation of free modules over $\mathbb F[x]$. We show how two existing algorithms for minimising such modules run…
A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with adaptive complexity for transmission over binary-input AWGN…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…
In this paper we provide a detailed description of Reed-Solomon (RS) codes, the most important algorithms for decoding them, and their use in concatenated coding systems for space applications. In the current literature there is scattered…