Related papers: Some New Non-binary Quantum Codes from One-generat…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices…
Cyclic codes have wide applications in data storage systems and communication systems. Employing two-prime Whiteman generalized cyclotomic sequences of order 6, we construct several classes of cyclic codes over the finite field GF}(q) and…
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of…
The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…
In this paper we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of voltage graphs and Paley graphs in the Galois field GF(pr), where p is a…
Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
Let $p$ be a prime and $\mathbb{F}_q$ be the finite field of order $q=p^m$. In this paper, we study $\mathbb{F}_q\mathcal{R}$-skew cyclic codes where $\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q$ with $u^2=u$. To characterize…
Let $f(u)$ be a polynomial of degree $m, m \geq 2,$ which splits into distinct linear factors over a finite field $\mathbb{F}_{q}$. Let $\mathcal{R}=\mathbb{F}_{q}[u]/\langle f(u)\rangle$ be a finite non-chain ring. In an earlier paper, we…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
Many classical constructions, such as Plotkin's and Turyn's, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other hand, form an algebraically rich structure class that contains many codes with best-known…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$…
In this paper, we give conditions for the existence of Hermitian self-dual $\Theta-$cyclic and $\Theta-$negacyclic codes over the finite chain ring $\mathbb{F}_q+u\mathbb{F}_q$. By defining a Gray map from $R=\mathbb{F}_q+u\mathbb{F}_q$ to…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…