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One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…

Information Theory · Computer Science 2020-03-24 Weiwei Wang , Jiantao Li

We construct quantum MDS codes with parameters $ [\![ q^2+1,q^2+3-2d,d ]\!] _q$ for all $d \leqslant q+1$, $d \neq q$. These codes are shown to exist by proving that there are classical generalised Reed-Solomon codes which contain their…

Quantum Physics · Physics 2021-01-15 Simeon Ball

An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition,…

Information Theory · Computer Science 2023-10-03 Ruhao Wan

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and…

Information Theory · Computer Science 2015-11-06 Baokun Ding , Tao Zhang , Gennian Ge

MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is…

Information Theory · Computer Science 2022-08-30 Ruhao Wan , Shixin Zhu , Jin Li

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…

Information Theory · Computer Science 2019-12-06 Weijun Fang , Fang-Wei Fu

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…

Information Theory · Computer Science 2020-02-17 Hualu Liu , Xiusheng Liu

Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters…

Information Theory · Computer Science 2018-07-17 Weijun Fang , Fang-Wei Fu

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…

Information Theory · Computer Science 2023-07-11 Ruhao Wan , Shixin Zhu

Based on the fundamental results on MDS self-dual codes over finite fields constructed via generalized Reed-Solomon codes \cite{JX} and extended generalized Reed-Solomon codes \cite{Yan}, many series of MDS self-dual codes with different…

Information Theory · Computer Science 2019-05-17 Aixian Zhang , Keqin Feng

In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…

Information Theory · Computer Science 2024-10-24 Puyin Wang , Jinquan Luo

In this paper, we produce some new classes of entanglement-assisted quantum MDS codes(EAQMDS codes for short) via generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes…

Information Theory · Computer Science 2020-08-27 Renjie Jin , Yiran Cao , Jinquan Luo

New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…

Information Theory · Computer Science 2012-08-14 Kenza Guenda , T. Aaron Gulliver

In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS…

Information Theory · Computer Science 2018-07-30 Khawla Labad , Honwei Liu , Jinquan Luo

A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider…

Information Theory · Computer Science 2020-05-26 Weijun Fang , Jun Zhang , Shu-Tao Xia1 , Fang-Wei Fu

MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…

Information Theory · Computer Science 2024-01-09 Yansheng Wu , Ziling Heng , Chengju Li , Cunsheng Ding

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…

Information Theory · Computer Science 2014-05-22 Liqi Wang , Shixin Zhu

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…

Information Theory · Computer Science 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes…

Information Theory · Computer Science 2019-09-18 Xiaolei Fang , Jinquan Luo
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