代數(shù)編碼及其應(yīng)用前沿系列講座
報(bào)告時(shí)間：2018年7月18日下午14:00-15:00
報(bào)告地點(diǎn)： X7503
主持人：周正春教授
Title: Factorizations of binomial polynomials and enumerations of LCD and Self-dual constacyclic codes
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 $\Bbb F_q$.
Bio: 岳勤，南京航空航天大學(xué)數(shù)學(xué)系教授，博士生導(dǎo)師。1996年中國科學(xué)技術(shù)大學(xué)數(shù)學(xué)系博士學(xué)位，師從馮克勤教授。曾訪問過意大利、韓國、香港和臺(tái)灣等地。研究方向?yàn)榇鷶?shù)數(shù)論，代數(shù)K理論，和代數(shù)編碼理論研究，發(fā)表論文70余篇，其中SCI文章60多篇，其中包括：J. Reine Angew. Math., Math. Z, IEEE Trans. Inform. Theory等刊物，主持4項(xiàng)國家自然科學(xué)基金和2項(xiàng)國際合作項(xiàng)目，江蘇省青藍(lán)工程學(xué)科帶頭人。
