Simplex and MacDonald Codes over $R_{q}$

In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring $R_{q}=mathbb{F}_{2}[u_{1},u_{2},ldots,u_{q}]/leftlangle u_{i}^{2}=0,u_{i}u_{j}=u_{j}u_{i}rightrangle$ for $q geq 2$. We also consider the construction of simplex and MacDonald codes of types $alpha$ and $beta$ over this ring.