Related papers: Algebraic Quantum Synchronizable Codes
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…
The efficiency of locally generating unitary designs, which capture statistical notions of quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and quantum information technologies. While there are extensive potent…
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be…
In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
In this paper, we investigate the algebraic structure for polycyclic codes over a specific class of serial rings, defined as $\mathscr R=R[x_1,\ldots, x_s]/\langle t_1(x_1),\ldots, t_s(x_s) \rangle$, where $R$ is a chain ring and each…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality…
The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length…
We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with…
Quantum Error Correction (QEC) codes store information reliably in logical qubits by encoding them in a larger number of less reliable qubits. The surface code, known for its high resilience to physical errors, is a leading candidate for…
In this paper we extend the work of Lisonek and Singh on construction X for quantum error-correcting codes to finite fields of order $p^2^ where p is prime. The results obtained are applied to the dual of Hermitian repeated root cyclic…
In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets,…
In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew…
Binary self-dual codes with large minimum distances, such as the extended Hamming code and the Golay code, are fascinating objects in the coding theory. They are closely related to sporadic simple groups, lattices and invariant theory. A…
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…
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…
In this paper, we first consider the iterated skew polynomial ring $\mathscr{R}[z_1;\tau_1,\delta_{\tau_1}]$\\$[z_2;\tau_2,\delta_{\tau_2}]$, where $\mathscr{R}$ is a finite ring with unity. Then we use this structure for the construction…