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.
机构:
Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Guo, Guanmin
Li, Ruihu
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Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Li, Ruihu
Liu, Yang
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Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Liu, Yang
Wang, Junli
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Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Jin, Renjie
Xie, Derong
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机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Xie, Derong
Luo, Jinquan
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机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
机构:
Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Guo, Guanmin
Li, Ruihu
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h-index: 0
机构:
Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Li, Ruihu
Liu, Yang
论文数: 0引用数: 0
h-index: 0
机构:
Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
Liu, Yang
Wang, Junli
论文数: 0引用数: 0
h-index: 0
机构:
Air Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R ChinaAir Force Engn Univ, Dept Basic Sci, Xian 710051, Shaanxi, Peoples R China
机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Jin, Renjie
Xie, Derong
论文数: 0引用数: 0
h-index: 0
机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Xie, Derong
Luo, Jinquan
论文数: 0引用数: 0
h-index: 0
机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China