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

Abstract: 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 and self-dual $(\delta+\alpha u^2)$-constacyclic codes are analyzed.