7月2日：岳勤

人：岳勤 教授

人：李成举 副教授

Let $\Bbb F_q$ be a finite field with order $q$  and $n$ a positive integer, where $q$ is a positive power of a prime $p$. Suppose that  the product of distinct prime factors of $n$ divides $q-1$, i.e. $rad(n)|(q-1)$. In this paper,  we explicitly factorize the polynomial $x^{n}-\lambda$ for each  $\lambda\in \Bbb F_q^*$. As applications, firstly, we   obtain  all $\lambda$-constacyclic codes and their dual codes of length $np^s$ over  $\Bbb F_q$; secondly, we determine all LCD cyclic codes and LCD negacyclic codes of length $n$ over $\Bbb F_q$; thirdly,  we  list all self-dual negacyclic codes of length $np^s$ over $\Bbb F_q$.