Professor Tor Helleseth, Department of Informatics, The University of Bergen, Norway
On ternary codes, PN, APN functions and open problems
In this talk we will study optimal ternary sequences which corresponding to the ternary cyclic code with the generator polynomial of the product of two irreducible polynomials over a prime field. In 2005 Ding, Carlet and Yuan showed that if a monomial is a monomial perfect nonlinear (PN) function then the corresponding code has a certain parameter. This talk will discuss generalizations of this result to cases where the monomial is almost perfect nonlinear (APN) as well as to other cases. In addition we give an overview of known results of values of exponents in monomial functions that give optimal codes with the same type of parameters and proof an open conjecture. Finally we provide a list of open problems of possible values of exponents that may also give optimal codes with these parameters.
Tor Helleseth (IEEE Fellow) received his Dr. Philos. degree in mathematics from the University of Bergen, Norway, in 1979. During the academic years 1977-1978 and 1992-1993 he was on sabbatical leave at the University of Southern California, Los Angeles, USA, and during 1979-1980 he was a Postdoctoral fellow at the Eindhoven University of Technology, The Netherlands. From 1981 to 1984 he was a researcher at the Chief Headquarters of Defense in Norway. Since 1984 has he has been a Professor at the Department of Informatics at the University of Bergen.
Professor Helleseth has twice served as an Associate Editor for IEEE Transactions on Information Theory, 1991-1993 for the area of Coding Theory and 2012-2014 for Sequences. He is on the editorial board for Designs, Codes and Cryptography (DCC), Advances in Mathematics of Communications (AMC), and Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences (CCDS), Journal of Mathematical Cryptology (JMC). Professor Helleseth has published more than 350 papers in international refereed journals and conferences in coding theory, cryptography and sequence designs, including more than 100 co-authors from more than 25 countries.
He was the program co-chair for Eurocrypt’93, IEEE Information Theory Workshop, ITW1997, ITW2007, and for Sequences and Their Applications, SETA’98, SETA’04, SETA’06, and SETA’12. Professor Helleseth was a coordinator of NISNet, a national network in information security, in Norway 2007-2011.
In 1997 he was elected IEEE Fellow for his "Contributions to Coding Theory and Cryptography" and in 2004 elected member of the Norwegian Academy of Science (Det Norske Videnskaps-Akademi). He served on the Board of Governors for the IEEE information Theory Society during 2007-2009. His interests include coding theory, cryptography, sequence designs, finite fields and discrete mathematics.
Invited by professor Guang Gong.