Some families of optimal quantum codes derived from constacyclic codes

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

doi:10.1080/03081087.2018.1432544

Cited by 6 publications

(4 citation statements)

References 47 publications

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“…Furthermore, it can be found from Tables 5-8 that under the same conditions of code length, d z and d x , this paper can construct some asymmetric EAQMDS codes with higher net rates that are not achieved in [18]. Finally, the parameters of the asymmetric EAQMDS codes constructed in this paper are more general than the quantum asymmetric codes constructed in [20][21][22][23][24]26], and some quantum codes have better parameters than the quantum asymmetric codes constructed using generalized RS codes in [29]. For example, the quantum codes [[96; 1, constructed in this paper.…”

Section: Codes Comparisonmentioning

confidence: 78%

“…However, the asymmetric EAQMDS codes in this paper require fewer entangled states, which means that the preparation cost and cost of quantum entangled states required in this paper are less. In addition, some quantum codes that do not exist in [18,[20][21][22][23][24][25][26][27][28][29] are obtained in this paper. Moreover, the minimum distance d z of some asymmetric EAQMDS codes constructed in this paper is much greater than q, indicating that such quantum codes have greater asymmetric error-correcting ability.…”

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confidence: 99%

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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Chen,

Fang,

Zhou

et al. 2023

Entropy

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Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of literature has investigated the construction of asymmetric QEC codes. However, the asymmetry of most QEC codes identified in the literature is limited by the dual-containing condition within the Calderbank-Shor-Steane (CSS) framework. This limitation restricts the exploration of their full potential in terms of asymmetry. In order to enhance the asymmetry of asymmetric QEC codes, we utilize entanglement-assisted technology and exploit the algebraic structure of cyclotomic cosets of constacyclic codes to achieve this goal. In this paper, we generalize the decomposition method of the defining set for constacyclic codes and apply it to count the number of pre-shared entangled states in order to construct four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes that satisfy the asymmetric entanglement-assisted quantum Singleton bound. Compared with the codes existing in the literature, the lengths of the constructed EAQMDS codes and the number of pre-shared entangled states are more general, and the codes constructed in this paper have greater asymmetry.

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Section: Codes Comparisonmentioning

confidence: 78%

mentioning

confidence: 99%

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Chen,

Fang,

Zhou

et al. 2023

Entropy

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“…10 . Here, the range of λ should be 1 ≤ λ ≤ q− 7 10 . In fact, if λ = q+3 10 , −qC s−(q+1)( 2q+1 5 +λ) = −qC s−(q+1)( q+1 2 ) = C s−(q+1) q−1 2 , then the required number of entangled states is 13.…”

Section: +1mentioning

confidence: 99%

“…In the quantum information and quantum computing, an important subject is to constuct some good quantum error-correcting codes (quantum codes for short) [3], [5], [7], [8], [15], [18], [30], [31], [35]- [37], [42]. Let q be a prime power, a q-ary quantum code of length n can be denoted as [[n, k, d]] q , where k represents the size of q k that is a q k -dimensional subspace of the q n -dimensional Hilbert space and d is the minimum distance.…”

Section: Introductionmentioning

confidence: 99%

Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

Chen

Feng

et al. 2019

IEEE Access

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Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that is larger than (q/2) + 1. The pre-shared entanglement between the sender and the receiver can improve the minimum distance of quantum MDS codes such that the minimum distance of some constructed codes achieves (q/2) + 1 or exceeds (q/2) + 1. Meanwhile, how to determine the required number of maximally entangled states to make the minimum distance of quantum MDS codes larger than (q/2) + 1 is an interesting problem in the quantum coding theory. In this paper, we utilize the decomposition of the defining set and q 2-cyclotomic cosets of constacyclic codes with the form q = αm + t or q = αm + α − t and n = (q 2 + 1/α) to construct some new families of entanglement-assisted quantum MDS codes that satisfy the entanglement-assisted quantum singleton bound, where q is an odd prime power and m is a positive integer, while both α and t are positive integers such that α = t 2 + 1. The parameters of these codes constructed in this paper are more general compared with the ones in the literature. Moreover, the minimum distance of some codes in this paper is larger than (q/2) + 1 or q + 1. INDEX TERMS Entanglement-assisted quantum codes, constacyclic codes, maximal-distance-separable (MDS) codes.

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On the Constructions of Quantum MDS Convolutional Codes

Huang

Zhu

2023

Int J Theor Phys

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Some families of optimal quantum codes derived from constacyclic codes

Cited by 6 publications

References 47 publications

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

On the Constructions of Quantum MDS Convolutional Codes

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