Quantum codes from Hermitian dual-containing constacyclic codes over $${\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}$$

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 $${\mathbb {R}}$$ .