EAQECCs derived from constacyclic codes over finite non-chain rings

Entanglement-assisted quantum error-correcting codes (EAQECCs) not only can boost the performance of stabilizer quantum error-correcting codes but also can be derived from arbitrary classical linear codes by loosing the self-orthogonal condition and using pre-shared entangled states between the sender and the receiver. It is a challenging work to construct optimal EAQECCs and determine the required number of pre-shared entangled states. Let \(\mathcal {R}_{t}=\mathbb {F}_{q^{2}}+v\mathbb {F}_{q^{2}}+v^{2}\mathbb {F}_{q^{2}}+\cdots +v^{t}\mathbb {F}_{q^{2}}\) ${\mathcal{R}}_t={\mathbb{F}}_{q^2}+v{\mathbb{F}}_{q^2}+v^2{\mathbb{F}}_{q^2}+\cdots +v^t{\mathbb{F}}_{q^2}$ , where q is an odd prime power and \(v^{t+1}=1\) $v^{t+1}=1$ . Based on the generalized Gray map that is provided from \(\mathcal {R}_{t}\) ${\mathcal{R}}_t$ to \(\mathbb {F}_{q^{2}}^{t+1}\) ${\mathbb{F}}_{q^2}^{t+1}$ , some new optimal EAQECCs are constructed from the Gray images of v-constacyclic codes over \(\mathcal {R}_{t}\) ${\mathcal{R}}_t$ . Compared with the known ones, our codes have better parameters.