Entanglement-assisted quantum MDS codes constructed from negacyclic codes

Chen, Jianzhang; Huang, Yuanyuan; Feng, Chunhui; Chen, Riqing

doi:10.1007/s11128-017-1750-4

Cited by 66 publications

(53 citation statements)

References 34 publications

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“…Recently, one can find in the literature some papers where the above formula (or formulae derived from it) are used for determining the entanglement corresponding to EAQECCs over arbitrary finite fields (see, for instance [6,9,17,21]). Although it holds for any finite field, we have found no proof in the literature and, thus, this work fills this gap.…”

Section: Introductionmentioning

confidence: 99%

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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Section: Introductionmentioning

confidence: 99%

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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“…Remark 1. The required number of maximally entangled states of the MDS EAQECCs reported in the literature (see for instance [7,10,13,18]) is fixed. However, the required number of maximally entangled states of the MDS EAQECCs defined by Theorem 4.5, 4.6, 4.7 and 4.8 can take almost all values.…”

Section: Constructions Of Entanglement-assisted Quantum Error Correctmentioning

confidence: 99%

MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

Luo

Cao

Chen

2019

IEEE Trans. Inform. Theory

112

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The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect to the Euclidean inner product. Several infinite families of MDS codes with arbitrary dimensional hull are presented. As an application, using these MDS codes with arbitrary dimensional hull, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters.

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“…In [8], Chen et al showed that the number of entangled states required for negacyclic codes is c = |Z 1 |, which is the same for constacyclic codes.…”

Section: Basics About Entanglement-assisted Quantum Codesmentioning

confidence: 98%

“…A definition for decomposition of the defining set of cyclic codes was given in [22]. In the following, we give a decomposition of the defining set of constacyclic codes, which is the same as negacyclic case defined by Chen et al in [8].…”

Section: Basics About Entanglement-assisted Quantum Codesmentioning

confidence: 99%

“…In [32], based on classical quaternary constacyclic codes, some parameters for quantum codes were obtained. In [8], a decomposition of the defining set of negacyclic codes has been proposed and by virtue of the proposed decomposition four classes of EAQEC codes have been constructed. Fan et al, have constructed five classes of entanglementassisted quantum MDS (EAQMDS for short) codes based on classical MDS codes by exploiting one or more pre-shared maximally entangled states [9].…”

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New entanglement-assisted MDS quantum codes from constacyclic codes

Koroglu

2019

Quantum Inf Process

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Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new classes of entanglement-assisted quantum maximum distance separable codes. Mathematics Subject Classification IntroductionQuantum error-correcting (QEC for brevity) codes were introduced for security of quantum information. Construction of good quantum codes via classical codes is a crucial task for quantum information and quantum computing (see Refs. [1,4,5,7,17,26,27,30,32] for example). A q-ary quantum code Q, denoted by parameters n, k, d q , is a q k dimensional subspace of the Hilbert space C q n . A quantum code C with parameters n, k, d q satisfy the quantum Singleton bound: k ≤ n − 2d + 2 (see [17]). If k = n − 2d + 2, then C is called a quantum maximum-distance-separable (MDS) code. In recent years, many researchers have been working to find quantum MDS codes via constacyclic codes (for instance, see [6,19,16,18,32,33]).Entanglement-assisted quantum error correcting (EAQEC for short) codes use pre-existing entanglement between the sender and receiver to improve

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Entanglement-assisted quantum MDS codes constructed from negacyclic codes

Cited by 66 publications

References 34 publications

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

New entanglement-assisted MDS quantum codes from constacyclic codes

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