Zeta functions for linear codes and formal weight enumerators

par Prof. Koji Chinen (Kindai University, Osaka, Japan)

mardi 22 nov. 2016, 10:45 → 11:45 Europe/Paris

Fokko du Cloux (ICJ)

In 1999, Iwan Duursma defined the zeta functions for linear codes and formulated their Riemann hypothesis. In particular, his conjecture that extremal self-dual codes satisfy the Riemann hypothesis attracted interests of both coding theorists and number theorists, because it claims in a sense that good codes satisfy the Riemann hypothesis. Later the speaker generalized Duursma's theory to the case of the formal weight enumerators. They are kinds of invariant polynomials which are close to the weight enumerators of self-dual codes and of which the special case were first introduced by Michio Ozeki. In this talk, an overview of Duursma's theory and some results on the zeta functions for formal weight enumerators are given.