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

Abstract: 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.