New quantum codes from two linear codes

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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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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Maximal entanglement entanglement-assisted quantum codes constructed from linear codes

Quantum Information Processing ◽

10.1007/s11128-014-0830-y ◽

2014 ◽

Vol 14 (1) ◽

pp. 165-182 ◽

Cited By ~ 20

Author(s):

Liangdong Lu ◽

Ruihu Li ◽

Luobin Guo ◽

Qiang Fu

Keyword(s):

Linear Codes ◽

Quantum Codes ◽

Maximal Entanglement

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Encoding classical information in gauge subsystems of quantum codes

International Journal of Quantum Information ◽

10.1142/s0219749921500416 ◽

2022 ◽

Author(s):

Andrew Nemec ◽

Andreas Klappenecker

Keyword(s):

Quantum Information ◽

Linear Codes ◽

Explicit Construction ◽

Quantum Codes ◽

Classical Information ◽

Hybrid Code ◽

Gauge Fixing ◽

Minimum Distances

In this paper, we show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

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New constructions of entanglement-assisted quantum MDS codes from negacyclic codes

International Journal of Quantum Information ◽

10.1142/s0219749919500229 ◽

2019 ◽

Vol 17 (03) ◽

pp. 1950022 ◽

Cited By ~ 6

Author(s):

Ruihu Li ◽

Guanmin Guo ◽

Hao Song ◽

Yang Liu

Keyword(s):

Minimum Distance ◽

Linear Codes ◽

Error Correcting Codes ◽

Optimal Number ◽

Mds Codes ◽

Quantum Codes ◽

General Statement ◽

Negacyclic Codes ◽

Maximum Distance Separable ◽

Quantum Error

When constructing quantum codes under the entanglement-assisted (EA) stabilizer formalism, one can ignore the limitation of dual-containing condition. This allows us to construct EA quantum error-correcting codes (QECCs) from any classical linear codes. The main contribution of this manuscript is to make a general statement for determining the optimal number of pre-shared qubits instead of presenting only specific cases. Let [Formula: see text] and [Formula: see text], where [Formula: see text] is an odd prime power, [Formula: see text] and [Formula: see text]. By deeply investigating the decomposition of the defining set of negacyclic codes, we generalize the number of pre-shared entanglement pairs of Construction (1) in Lu et al. [Quantom Inf. Process. 17 (2018) 69] from [Formula: see text] to arbitrary even numbers less than or equal to [Formula: see text]. Consequently, a series of EA quantum maximum distance separable (EAQMDS) codes can be produced. The absolute majority of them are new and the minimum distance can be up to [Formula: see text]. Moreover, this method can be applied to construct many other families of EAQECCs with good parameters, especially large minimum distance.

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