  Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This
article studies $(1-2u^k)$-constacyclic codes over the ring
$\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$
where $u^{k+1}=u$. We illustrate the generator polynomials and investigate the
structural properties of these codes via decomposition theorem.
