LAUSR

Let $$R={\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$R=Fq+vFq+v2Fq be a finite non-chain ring, where q is an odd prime power and $$v^3=v$$v3=v. In this paper, we propose two methods of constructing quantum codes from $$(\alpha +\beta v+\gamma v^{2})$$(α+βv+γv2)-constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank–Shor–Steane construction from Euclidean dual-containing $$(\alpha +\beta v+\gamma v^{2})$$(α+βv+γv2)-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing $$(\alpha +\beta v+\gamma v^{2})$$(α+βv+γv2)-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained.