In this paper we construct quantum codes over \(\mathbb F_p\) by using cyclic and \(\lambda \)-cyclic codes over the ring \(R=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^2\mathbb {F}_{p}+v\mathbb {F}_{p} +uv\mathbb {F}_{p}+u^2v\mathbb {F}_{p}+v^2\mathbb {F}_{p}+uv^2\mathbb {F}_{p} +u^2v^2\mathbb {F}_{p}\) where \(v^3=v , u^3=u , uv=vu\) and p is an odd prime integer. Using the idempotent decomposition method, we have given the parameters of the quantum code. Moreover, the structure of cyclic and \(\lambda \)-constacyclic codes over R is studied. Some quantum codes over \(\mathbb {F}_p\) are given.

在本文中，我们通过在环\（R = \ mathbb {F} _ {p} + u \ mathbb {F上）使用循环和\（\ lambda \） -循环码来构造\（\ mathbb F_p \）上的量子代码} _ {p} + u ^ 2 \ mathbb {F} _ {p} + v \ mathbb {F} _ {p} + uv \ mathbb {F} _ {p} + u ^ 2v \ mathbb {F} _ {p} + v ^ 2 \ mathbb {F} _ {p} + uv ^ 2 \ mathbb {F} _ {p} + u ^ 2v ^ 2 \ mathbb {F} _ {p} \）其中\（v ^ 3 = v，u ^ 3 = u，uv = vu \）并且p是一个奇质数整数。使用幂等分解方法，我们给出了量子代码的参数。此外，还研究了R上的循环和\（\ lambda \）常数代码的结构。给出了\（\ mathbb {F} _p \）上的一些量子代码。