On quantum and LCD codes from the cyclic codes over the ring \(\mathbb {F}_q[\textsf{u}, \textsf{v},\textsf{w}]/\langle \textsf{u}^3-\textsf{u},\textsf{v}^2-\textsf{v}, \textsf{w}^2-\textsf{w}, \textsf{u}\textsf{v}, \textsf{v}\textsf{u}, \textsf{u}\textsf{w}, \textsf{w}\textsf{u}, \textsf{v}\textsf{w}-\textsf{w}\textsf{v} \rangle \)

For an odd prime p and a positive integer r, let \(q=p^r\) $q=p^r$ . The objective of this article is to study cyclic codes over the ring \(\mathcal {S}=\mathbb {F}_q[\textsf{u}, \textsf{v},\textsf{w}]/\langle \textsf{u}^3-\textsf{u},\textsf{v}^2-\textsf{v}, \textsf{w}^2-\textsf{w}, \textsf{u}\textsf{v}, \textsf{v}\textsf{u}, \textsf{u}\textsf{w}, \textsf{w}\textsf{u}, \textsf{v}\textsf{w}-\textsf{w}\textsf{v} \rangle \) $\mathcal{S}={\mathbb{F}}_q[\mathsf{u},\mathsf{v},\mathsf{w}]/⟨{\mathsf{u}}^3-\mathsf{u},{\mathsf{v}}^2-\mathsf{v},{\mathsf{w}}^2-\mathsf{w},\mathsf{u}\mathsf{v},\mathsf{v}\mathsf{u},\mathsf{u}\mathsf{w},\mathsf{w}\mathsf{u},\mathsf{v}\mathsf{w}-\mathsf{w}\mathsf{v}⟩$ and to construct new and better quantum and LCD codes from them. We give the structure of cyclic codes over the ring \(\mathcal {S}\) $\mathcal{S}$ and obtain dual-containing codes over \(\mathbb {F}_q\) ${\mathbb{F}}_q$ as the Gray images of dual-containing cyclic codes over \(\mathcal {S}\) $\mathcal{S}$ . Using these dual-containing codes, we obtain quantum codes and determine their parameters using the decomposition of cyclic codes over the ring \(\mathcal {S}\) $\mathcal{S}$ . We provide many new and better-than-existing quantum codes. We also give a method to obtain linear complementary dual (LCD) codes over \(\mathcal {S}\) $\mathcal{S}$ using the decomposition of cyclic codes over the ring \(\mathcal {S}\) $\mathcal{S}$ . We obtain some optimal and best-known linear codes as Gray images of LCD codes over \(\mathcal {S}\) $\mathcal{S}$ .