Maximal entanglement entanglement-assisted quantum codes constructed from linear codes

Entanglement-assisted quantum error correcting code (EAQECC) is a generalization of standard stabilizer quantum code. Maximal entanglement EAQECCs can achieve the EA-hashing bound asymptotically. In this work, we give elementary recursive constructions of quaternary zero radical codes with dual distance three for all n ≥ 4. Consequently, good maximal entanglement EAQECCs of minimum distance three for such length n are obtained. Almost all of these EAQECCs are optimal or near optimal according to the EA-quantum Hamming bound.

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Quantum codes over rings

International Journal of Quantum Information ◽

10.1142/s0219749914500208 ◽

2014 ◽

Vol 12 (04) ◽

pp. 1450020 ◽

Cited By ~ 4

Author(s):

Kenza Guenda ◽

T. Aaron Gulliver

Keyword(s):

Linear Codes ◽

Error Correcting Codes ◽

Codes Over Rings ◽

Quantum Codes ◽

Matrix Product ◽

Frobenius Rings ◽

Linear Codes Over Rings ◽

Generalized Gray Map ◽

Css Construction ◽

Quantum Error

This paper considers the construction of quantum error correcting codes from linear codes over finite commutative Frobenius rings. We extend the Calderbank–Shor–Steane (CSS) construction to these rings. Further, quantum codes are extended to matrix product codes. Quantum codes over 𝔽pk are also obtained from linear codes over rings using the generalized Gray map.

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Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication

Mathematics ◽

10.3390/math8091495 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1495

Author(s):

Yansheng Wu ◽

Yoonjin Lee

Keyword(s):

Linear Codes ◽

Sufficient Conditions ◽

Quantum Codes ◽

Binary Linear Codes ◽

Hamming Codes ◽

Orthogonal Codes ◽

Css Codes ◽

Css Construction ◽

Necessary And Sufficient ◽

Quantum Error

It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

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New Non-Binary Quantum Codes Derived From a Class of Linear Codes

IEEE Access ◽

10.1109/access.2019.2899383 ◽

2019 ◽

Vol 7 ◽

pp. 26418-26421 ◽

Cited By ~ 5

Author(s):

Jian Gao ◽

Yongkang Wang

Keyword(s):

Linear Codes ◽

Quantum Codes

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A New Method of Constructing Binary Quantum Codes From Arbitrary Quaternary Linear Codes

IEEE Communications Letters ◽

10.1109/lcomm.2019.2961353 ◽

2020 ◽

Vol 24 (3) ◽

pp. 472-476 ◽

Cited By ~ 1

Author(s):

Junli Wang ◽

Ruihu Li ◽

Jingjie Lv ◽

Hao Song

Keyword(s):

Linear Codes ◽

New Method ◽

Quantum Codes ◽

Quaternary Linear Codes

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Maximal entanglement entanglement-assisted quantum codes from quaternary BCH codes

2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC) ◽

10.1109/iaeac.2015.7428647 ◽

2015 ◽

Cited By ~ 1

Author(s):

Liangdong Lv ◽

Ruihu Li ◽

Qiang Fu ◽

Xueliang Li

Keyword(s):

Bch Codes ◽

Quantum Codes ◽

Maximal Entanglement

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On the construction of optimal asymmetric quantum codes

International Journal of Quantum Information ◽

10.1142/s0219749914500178 ◽

2014 ◽

Vol 12 (03) ◽

pp. 1450017 ◽

Cited By ~ 5

Author(s):

Liqi Wang ◽

Shixin Zhu

Keyword(s):

Linear Codes ◽

Quantum Codes ◽

Constacyclic Codes ◽

Asymmetric Quantum ◽

Asymmetric Quantum Codes

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.

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