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