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Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. Thisarticle 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 thestructural properties of these codes via decomposition theorem.

$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$