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Erschienen in:
01.03.2021
Quantum codes from Hermitian dual-containing constacyclic codes over \({\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}\)
Erschienen in: Quantum Information Processing | Ausgabe 3/2021
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Abstract
Let \({\mathbb {R}}\) be the finite non-chain ring \({\mathbb {F}}_{{ q}^{2}}+{v}{\mathbb {F}}_{{ q}^{2}}\), where \({v}^{2}={v}\) and q is an odd prime power. In this paper, we study quantum codes over \({\mathbb {F}}_{{ q}}\) from constacyclic codes over \({\mathbb {R}}\). We define a class of Gray maps, which preserves the Hermitian dual-containing property of linear codes from \({\mathbb {R}}\) to \({\mathbb {F}}_{{ q}^{2}}\). We study \({\alpha }(1-2v)\)-constacyclic codes over \({\mathbb {R}}\), and show that the images of \(\alpha (1-2v)\)-constacyclic codes over \({\mathbb {R}}\) under the special Gray map are \(\alpha ^{2}\)-constacyclic codes over \({\mathbb {F}}_{{ q}^{2}}\). Some new non-binary quantum codes are obtained via the Gray map and the Hermitian construction from Hermitian dual-containing \(\alpha (1-2v)\)-constacyclic codes over \({\mathbb {R}}\).