Related papers: Distinguishers for Skew and Linearized Reed-Solomo…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
MDS codes have garnered significant attention due to their wide applications in practice. To date, most known MDS codes are equivalent to Reed-Solomon codes. The construction of non-Reed-Solomon (non-RS) type MDS codes has emerged as an…
In this paper, we study a class of twisted generalized Reed-Solomon (TGRS) codes with general l twists. A sufficient and necessary condition for the TGRS codes to be MDS or l-MDS (l<k and l<n-k) is determined. A sufficient and necessary…
Folded Reed-Solomon (FRS) codes are variants of Reed-Solomon codes, known for their optimal list decoding radius. We show explicit FRS codes with rate $R$ that can be list decoded up to radius $1-R-\epsilon$ with lists of size…
Deep holes play an important role in the decoding of generalized Reed-Solomon codes. Recently, Wu and Hong \cite{WH} found a new class of deep holes for standard Reed-Solomon codes. In the present paper, we give a concise method to obtain a…
In recent years, the construction of non-GRS type linear codes has attracted considerable attention due to that they can effectively resist both the Sidelnikov-Shestakov attack and the Wieschebrink attack. Constructing linear complementary…
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…
Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a major role in practical error control for network coding. This paper presents new encoding and decoding algorithms for Gabidulin codes based on low-complexity…
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring…
Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be…
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…
In this paper, deep holes of Reed-Solomon (RS) codes are studied. A new class of deep holes for generalized affine RS codes is given if the evaluation set satisfies certain combinatorial structure. Three classes of deep holes for projective…
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,…
In a recent breakthrough [BGM23, GZ23, AGL23], it was shown that randomly punctured Reed-Solomon codes are list decodable with optimal list size with high probability, i.e., they attain the Singleton bound for list decoding [ST20, Rot22,…
Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code and the error-correction radius. In 2024, Bergamaschi,…
Determining deep holes is an important topic in decoding Reed-Solomon codes. Let $l\ge 1$ be an integer and $a_1,\ldots,a_l$ be arbitrarily given $l$ distinct elements of the finite field ${\bf F}_q$ of $q$ elements with the odd prime…
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent…
We consider the weight distributions of the cosets of weight 2 of the generalized $[q+1,q+2-d,d]_q$ doubly extended Reed-Solomon codes (GDRS) of minimum distance $d\ge5$, over the finite field $\mathbb{F}_q$ with $q$ elements. For a GDRS…