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We propose an efficient algorithm to find a Reed-Solomon (RS) codeword at a distance within the covering radius of the code from any point in its ambient Hamming space. To the best of the authors' knowledge, this is the first attempt of its…
We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank metric. The proposed interpolation-based scheme…
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as…
Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…
Reed-Solomon (RS) codes are widely used in distributed storage systems. In this paper, we study the repair bandwidth and sub-packetization size of RS codes. The repair bandwidth is defined as the amount of transmitted information from…
In this paper, we study the Hermitian hulls of generalized Reed-Solomon (GRS) codes over finite fields. For a given class of GRS codes, by extending the length, increasing the dimension, and extending the length and increasing the dimension…
Coding for distributed storage gives rise to a new set of problems in coding theory related to the need of reducing inter-node communication in the system. A large number of recent papers addressed the problem of optimizing the total amount…
In this paper, we prove that explicit FRS codes and multiplicity codes achieve relaxed generalized Singleton bounds for list size $L\ge1.$ Specifically, we show the following: (1) FRS code of length $n$ and rate $R$ over the alphabet…
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary…
In 2017, Beelen et al. firstly introduced twisted generalized Reed-Solomon (in short, TGRS) codes, and constructed a large subclass of MDS TGRS codes. Later, they proved that TGRS code is non-GRS when the code rate is less than one half. In…
We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the…
In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…
We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal…
The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible configuration of zeros for an MDS code. The recently emerging…
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a…
Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon…
This paper develops an algorithmic approach for obtaining approximate, numerical estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which satisfy a given constraint. Our algorithm is based on a statistical…
List recovery of error-correcting codes has emerged as a fundamental notion with broad applications across coding theory and theoretical computer science. Folded Reed-Solomon (FRS) and univariate multiplicity codes are explicit…
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…
Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…