Related papers: Row-Column Twisted Reed-Solomon codes
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…
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…
Twisted generalized Reed-Solomon (TGRS) codes constitute an interesting family of evaluation codes, containing a large class of maximum distance separable codes non-equivalent to generalized Reed-Solomon (GRS) ones. Moreover, the Schur…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
Maximum distance separable (MDS) codes are considered optimal because the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are likely the generalized Reed-Solomon (GRS) codes. In 1989, Roth…
Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes…
We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new…
Maximum distance separable (in short, MDS), near MDS (in short, NMDS), and self-orthogonal codes play a pivotal role in algebraic coding theory, particularly in applications such as quantum communications and secret sharing scheme.…
We investigate a natural subfamily of twisted linearized Reed--Solomon (TLRS) codes in the sum-rank metric, where the twist is applied only to the constant term. We establish a simple necessary and sufficient condition for these codes to be…
This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns…
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…
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…
The hull of a linear code is defined to be the intersection of the code and its dual. When the size of the hull is small, it has been proved that some algorithms for checking permutation equivalence of two linear codes and computing the…
In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes $\mathcal{C}_{\bm \alpha, \bm t, \bm h, \bm \eta}$…
Twisted generalized Reed-Solomon (TGRS) codes are an extension of the generalized Reed-Solomon (GRS) codes by adding specific twists, which attract much attention recently. This paper presents an in-depth and comprehensive investigation of…
Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent…
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…
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, by calculating the dual code of the Schur square for the standard twisted Reed-Solomon code, we give a sufficient and necessary condition for the generalized twisted Reed-Solomon code with $h+t\le k-1$ to be self-orthogonal,…
New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed…