## HAI QUANG DINH: On the distance distributions of repeated-root constacyclic codes of multi-symbol read channels发布日期：2019-07-24  字号：大 中 小  【打印】

HAI QUANG DINH 教授

H. Q. DINH is a professor in Applied Mathematics at the Department of Mathematical Sciences, Kent State University, USA. After completed his B.Sc. (1998), M.Sc. (2000), and Ph.D. (2003) in Mathematics at Ohio University, USA, he worked one year as a visiting professor at North Dakota State University, USA. Since 2004, Prof. Dinh has been working at Kent State University as a tenure professor in mathematics. Prof. Dinh research interests include Algebra and Coding Theory. Since 2004, he has published more than 75 papers at high level SCI(E) research journals such as Journal of Algebra, Journal of Pure and Applied Algebra, IEEE Transactions on Information Theory, IEEE Communication Letters, Finite Fields and Their Applications, Applicable Algebra in Engineering Communication and Computing, Discrete Applied Mathematics. Prof. Dinh has been a well known invited/keynote speaker at numerous international conferences and mathematics colloquium. Other than universities in the US, he also gave many honorary tutorial lectures at international universities in China, Indonesia, Kuwait, Mexico, Singapore, Thailand, Vietnam.

Let $p$ be a prime, $s$ and $m$ be positive integers and $\lambda$ be a nonzero element of the finite field $\mathbb{F}_{p^m}$. The $\lambda$-constacyclic codes of length $p^s$ over $\mathbb{F}_{p^m}$ are linearly ordered under set theoretic inclusion as ideals of the chain ring $\mathbb{F}_{p^m}[x]/\langle x^{p^s}-\lambda \rangle$. Using this structure, the Hamming, symbol-pair, symbol-tripple, and more generally, the $b$-symbol distances, of all such $\lambda-$constacyclic codes are established in this talk. All maximum distance separable (MDS) $b$-symbol constacyclic codes of length $p^s$ are also determined as an application. We will also discuss further generalizations in term of code-lengths and alphabets.

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