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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

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…

Quantum Physics · Physics 2009-11-13 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

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

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

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

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

In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.

Information Theory · Computer Science 2021-05-26 Xiusheng Liu , Hualu Liu , Long Yu

Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…

Information Theory · Computer Science 2022-11-01 Meng Cao

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

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

Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum…

Information Theory · Computer Science 2025-03-03 Diego Ruano , Rodrigo San-José

There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…

Information Theory · Computer Science 2021-12-14 Lin Sok

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

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

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

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

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

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…

Quantum Physics · Physics 2011-10-20 Markus Grassl , Willi Geiselmann , Thomas Beth

In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC.…

Information Theory · Computer Science 2025-12-19 Oisin Campion , Fernando Hernando , Gary McGuire

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…

Information Theory · Computer Science 2024-03-19 Xiujing Zheng , Liqi Wang , Shixin Zhu
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