Advertisement
Published in:
01-03-2021
Quantum codes from Hermitian dual-containing constacyclic codes over \({\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}\)
Published in: Quantum Information Processing | Issue 3/2021
Log inActivate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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 \({\mathbb {R}}\).