Prof.  HAI Q  DINH
Department of Mathematical Sciences, Kent State University,  USA

Title: Quantum maximum distance separable and synchronizable codes from a class of cyclic codes over finite fields

Abstract:

In this talk, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length $2p^s$ over $\mathbb F_{p^m}$ are established. As an application, all quantum MDS (briefly, qMDS) codes are constructed from cyclic and negacyclic codes of length $2p^s$ over finite fields using the Calderbank-Shor-Steane (briefly, CSS) and Hermitian constructions. These codes are new in the sense that their parameters are different from all the previous constructions. Furthermore, quantum synchronizable codes (briefly, QSCs) are obtained from cyclic codes of length $2p^s$ over $\mathbb F_{p^m}$. To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes. Open directions for further research will also be discussed.

Biography:

Dr. HAI Q. DINH is a professor in Mathematics at the Department of Mathematical Sciences, Kent State University, USA. After completing his B.Sc. (1998) Summa Cum Laude, 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 full professor in mathematics. Prof. Dinh research interests include Algebra and Coding Theory. Since 2004, he has published more than 120 papers at high level SCI(E) research journals such as Journal of Algebra, Journal of Pure and Applied Algebra, IEEE Transactions in 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 with more than 100 invited talks. Other than universities in the US, he also gave many honorary tutorial lectures, ranging from 8 to 30 hours, at international universities in China, Indonesia, Kuwait, Mexico, Singapore, Thailand, and Vietnam.