Related papers: The $(+)$-extended twisted generalized Reed-Solomo…
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…
The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we…
We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a lattice. By solving this problem, we provide explicit formulas…
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…
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…
We consider the $[q+1,q-3,5]_q3$ generalized doubly-extended Reed-Solomon code of codimension $4$ as the code associated with the twisted cubic in the projective space $\mathrm{PG}(3,q)$. Basing on the point-plane incidence matrix of…
The deep holes of a linear code are the vectors that achieve the maximum error distance (covering radius) to the code. {Determining the covering radius and deep holes of linear codes is a fundamental problem in coding theory. In this paper,…
Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth…
Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from…
The deep hole problem is a fundamental problem in coding theory, and it has many important applications in code constructions and cryptography. The deep hole problem of Reed-Solomon codes has gained a lot of attention. As a generalization…
In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-$\ell$ MDS code, denoted by $\operatorname{MDS}(\ell)$, has the property that any $\ell$ subspaces formed from…
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…
Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.
We study the distinguishability of linearized Reed-Solomon (LRS) codes by defining and analyzing analogs of the square-code and the Overbeck distinguisher for classical Reed-Solomon and Gabidulin codes, respectively. Our main results show…
Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against $\ell_p$ adversaries,…
It is well-known that Reed-Solomon codes and extended Reed-Solomon codes are two special classes of MDS codes with wide applications in practice. The complete weight enumerators of these codes are very important for determining the…
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 this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…