Let p be an odd prime and m be a positive integer, q=pm\documentclass[12pt]{minimal}
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\begin{document}$$q=p^m$$\end{document}, R=Fq+uFq\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {R}}={\mathbb {F}}_q+u{\mathbb {F}}_q$$\end{document} with u2=u\documentclass[12pt]{minimal}
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\begin{document}$$u^2=u$$\end{document}, and S=Fq+uFq+vFq\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {S}}={\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$\end{document} with u2=u,v2=v,uv=vu=0\documentclass[12pt]{minimal}
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\begin{document}$$u^2=u, v^2=v, uv=vu=0$$\end{document} and Λ=(λ1,λ2,λ3)∈FqRS\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda =(\lambda _1,\lambda _2,\lambda _3)\in {\mathbb {F}}_q{\mathcal {R}}{\mathcal {S}}$$\end{document}. In this paper, we study the algebraic structure of constacyclic codes over R\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {R}}$$\end{document} and S\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {S}}$$\end{document}. Further, we discuss the structure of FqRS\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_q{\mathcal {R}}{\mathcal {S}}$$\end{document}-Λ\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda $$\end{document}-constacyclic codes of block length (α,β,γ)\documentclass[12pt]{minimal}
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\begin{document}$$(\alpha ,\beta ,\gamma )$$\end{document}. This family of codes can be viewed as S[x]\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {S}}[x]$$\end{document}-submodules of Fq[x]⟨xα-λ1⟩×R[x]⟨xβ-λ2⟩×S[x]⟨xγ-λ3⟩\documentclass[12pt]{minimal}
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\begin{document}$$\frac{{\mathbb {F}}_q[x]}{\langle x^{\alpha }-\lambda _1\rangle }\times \frac{{\mathcal {R}}[x]}{\langle x^{\beta }-\lambda _2\rangle }\times \frac{{\mathcal {S}}[x]}{\langle x^{\gamma }-\lambda _3\rangle }$$\end{document}. The generator polynomials of this family of codes are discussed. As application, we discuss the construction of quantum error-correcting codes (QECCs) from constacyclic codes over FqRS\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_q{\mathcal {R}}{\mathcal {S}}$$\end{document} and obtain several new QECCs from this study.
