Quantum Codes from Cyclic Codes over the Ring \(R = \mathbbm {F}_{q} + u\mathbbm {F}_{q} + v\mathbbm {F}_{q} +uv \mathbbm {F}_{q} + v^{2}\mathbbm {F}_{q}+ uv^{2}\mathbbm {F}_{q}\)

In this paper, the structure of cyclic codes the ring \(R = \mathbbm {F}_{q} + u\mathbbm {F}_{q} + v\mathbbm {F}_{q} +uv \mathbbm {F}_{q} + v^{2}\mathbbm {F}_{q}+ uv^{2}\mathbbm {F}_{q}\) where \( uv = vu,\,u^{2}= u,\, v^{3} = v\) , is used to obtain quantum codes over \(\mathbbm {F}_{q}\) . We have given the parameters of these codes by using the idempotent decomposition.