Negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$

Let $p$ be an odd prime. The algebraic structure of all negacyclic codes of length $8p^s$ over the finite commutative chain ring $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ into 5 cases, i.e., $p^m\equiv 1 \pmod{16}$, $p^m\equiv 3,11 \pmod{16}$, $p^m\equiv 5,13 \pmod{16}$, $p^m\equiv 7,15 \pmod{16}$ and $p^m\equiv 9 \pmod{16}$. From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.