All $\alpha +u\beta$-constacyclic codes of length $n{p}^s$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$

Wei Zhao, Xilin Tang, Ze Gu

Let ${\mathbb{F}}_{p^m}$ be a finite field with cardinality $p^m$ and $R={\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ with $u^2=0$. We aim to determine all $\alpha +u\beta$-constacyclic codes…