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Quantum Information Processing

-linear skew constacyclic codes and their application of constructing quantum codes

  • 01-07-2020
Published in:
Authors
Juan Li
Jian Gao
Fang-Wei Fu
Fanghui Ma
Published in
Quantum Information Processing | Issue 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.

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previous article The images of constacyclic codes and new quantum codes
next article Benchmarking the quantum approximate optimization algorithm
Title
-linear skew constacyclic codes and their application of constructing quantum codes
Authors
Juan Li
Jian Gao
Fang-Wei Fu
Fanghui Ma
Publication date
01-07-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02700-x
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