Title: 1. Codes from bent functions over finite fields 

　　     2. New LRC codes from good polynomials 

　　Speaker: Prof.  Sihem Mesnager ( University of Paris VIII) 

　　Time: 2016年9月14日，上午10:00-11:30 

　　Address: Room 3224 

　　Abstract:                                          

　　Error correcting codes are widely studied by researchers and employed by engineers. They have long been known to have applications in computer and communication systems, data storage devices (starting from the use of Reed Solomon codes in CDs) and consumer electronics. A lot of progress has been made on the constructions of linear codes with few weights. Such codes have applications in secret sharing authentication codes, association schemes and strongly regular graphs. 

　　Certain special types of functions over finite fields are closely related to linear or nonlinear codes. In the past decade, a lot of progress on interplays between special functions and codes has been made. In particular, APN functions, planar functions, Dickson polynomials, and q-polynomials were employed to construct linear codes with optimal or almost optimal parameters. Recently, several new approaches to constructing linear codes with special types of functions were proposed, and a lot of linear codes with excellent parameters were obtained. 

　　It is well-known that Kerdock codes are constructed from bent functions. Very recently, some authors have highlighted that bent functions lead to the construction of interesting linear codes (in particular, linear codes with few weights). This talk is devoted to linear codes from bent functions. We shall present the state of the art as well as our recent contributions in this topic.We will present two generic constructions of linear codes involving special functions and investigate constructions of good linear codes based on the generic constructions involving bent functions over finite fields. More specifically, we shall give more details on our recent (2016) results on linear codes with few weights from weakly regular bent functions based on a generic construction. 

　　Sihem Mesnager's Short Bio: 

　　Sihem Mesnager received his PhD from the University of Pierre and Marie Curie (Paris VI). She is currently a professor with Telecom ParisTech and associate professor in Mathematics at University of Paris VIII. Her research interests include cryptography, Boolean functions, coding theory, Commutative algebra and computational algebraic geometry. She has published more 70 papers in international journals and proceedings of international conferences. She also wrote two books on bent functions and error correcting codes, respectively.