$(1-2u^2)$-constacyclic codes over ${\mathbb{F}}_p+u{\mathbb{F}}_p+u^2{\mathbb{F}}_p$

Let ${\mathbb{F}}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring ${\mathbb{F}}_p+u{\mathbb{F}}_p+u^2{\mathbb{F}}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.