# Factorizations of Binomial Polynomials and Enumerations of LCD and Self-dual Constacyclic Codes

 Title Factorizations of Binomial Polynomials and Enumerations of LCD and Self-dual Constacyclic Codes Speaker 岳勤 教授 DateTime 2018年10月12日（星期五）下午16:00—17:00 Place 六号楼二楼会议室 Abstract 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 $\Bbb F_q$. Brief Introduction to Speaker 岳勤，南京航空航天大学数学系教授，博士生导师。1996年中国科学技术大学数学系博士学位。曾访问过意大利、韩国、香港和台湾等地。研究方向为代数数论和代数编码理论研究，发表论文70余篇，其中SCI文章60几篇，其中包括：J. Reine Angew. Math., Math. Z, IEEE Trans. Inform. Theory等刊物，主持4项国家自然科学基金和2项国际合作项目，江苏省青蓝工程学科带头人。