Quantum codes over Fq from α+βu+γv+δuv+ηu2+θv2+λu2v+μuv2+νu2v2- constacyclic codes

Abstract

The goal of this work is the construction of quantum codes over $\mathbb{F}_{q}$ by using $\alpha+\beta u+\gamma v+\delta u v+\eta u^{2}+\theta v^{2}+\lambda u^{2} v+$ $\mu u v^{2}+\nu u^{2} v^{2}$-constacyclic codes over the ring $R=\mathbb{F}_{q}+\mathbb{F}_{q} u+$ $\mathbb{F}_{q} v+\mathbb{F}_{q} u v+\mathbb{F}_{q} u^{2}+\mathbb{F}_{q} v^{2}+\mathbb{F}_{q} u^{2} v+\mathbb{F}_{q} u v^{2}+\mathbb{F}_{q} u^{2} v^{2}$. We give the structure of $\alpha+\beta u+\gamma v+\delta u v+\eta u^{2}+\theta v^{2}+\lambda u^{2} v+\mu u v^{2}+\nu u^{2} v^{2}$. constacyclic and obtain self-orthogonal codes. We decompose a constacyclic code over $\mathbb{F}_{q}+\mathbb{F}_{q} u+\mathbb{F}_{q} v+\mathbb{F}_{q} u v+\mathbb{F}_{q} u^{2}+\mathbb{F}_{q} v^{2}+$ $\mathbb{F}_{q} u^{2} v+\mathbb{F}_{q} u v^{2}+\mathbb{F}_{q} u^{2} v^{2}$ into constacyclic codes over $\mathbb{F}_{q}$. This decomposition makes it possible to give the parameters of the corresponding quantum code.