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Quantum Information Processing

Erschienen in:

01.07.2020

\({\mathbb {F}}_qR\)-linear skew constacyclic codes and their application of constructing quantum codes

verfasst von: Juan Li, Jian Gao, Fang-Wei Fu, Fanghui Ma

Erschienen in: Quantum Information Processing | Ausgabe 7/2020

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Abstract

Let q be a prime power with \(\mathrm{gcd}(q,6)=1\). Let \(R={\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+v{\mathbb {F}}_{q^2}+uv{\mathbb {F}}_{q^2}\), where \(u^2=u\), \(v^2=v\) and \(uv=vu\). In this paper, we give the definition of linear skew constacyclic codes over \({\mathbb {F}}_{q^2}R\). By the decomposition method, we study the structural properties and determine the generator polynomials and the minimal generating sets of linear skew constacyclic codes. We define a Gray map from \({\mathbb {F}}_{q^2}^{\alpha }\times R^{\beta }\) to \({\mathbb {F}}_{q^2}^{\alpha +4\beta }\) preserving the Hermitian orthogonality, where \(\alpha \) and \(\beta \) are positive integers. As an application, by Hermitian construction, we obtain some good quantum error-correcting codes.

Vorheriger Artikel The images of constacyclic codes and new quantum codes

Nächster Artikel Benchmarking the quantum approximate optimization algorithm

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Titel: -linear skew constacyclic codes and their application of constructing quantum codes
verfasst von: Juan Li
Jian Gao
Fang-Wei Fu
Fanghui Ma
Publikationsdatum: 01.07.2020
Verlag: Springer US
Erschienen in: Quantum Information Processing / Ausgabe 7/2020
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-020-02700-x

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