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Southwest Jiaotong University School of Mathematics

信息与计算科学系

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【代数编码及其应用前沿系列讲座】南开大学符方伟教授学术报告

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Title:On the Minimum Average Distance of Binary 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 $\Bbb F_q$.