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For units $\delta$ and $\alpha$ in $\F_{p^m}$, the structure of$(\delta+\alpha u^2)$-constacyclic codes of length $p^k$ over$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ is studied andself-dual $(\delta+\alpha u^2)$-constacyclic codes are analyzed.

A note on complete classification of $(\delta+\alpha u^2)$-constacyclic codes of length $p^k$ over $\F_{p^m}+u\F_{p^m}+u^2\F_{p^m}$