Algebra Seminar talk
Are normal bent functions normal?
Since their introduction by Rothaus in 1976, Boolean bent functions and bent functions from F_p^n to F_p, p odd, attracted a lot of attention due to connections to many areas like combinatorics, coding theory or cryptography. Several constructions of bent functions are known, most of them yield bent functions which exhibit certain properties: Whereas asymptotically almost all Boolean functions are not weakly normal, most constructions of Boolean bent functions yield weakly normal functions, i.e. Boolean functions in dimension n = 2m which are affine on an m-dimensional subspace.
The classical constructions of p-ary bent functions yield so called weakly regular bent functions, many of which are also normal (or at least almost weakly normal). In this talk some recent results on normality and regularity of bent functions are discussed. For instance we present constructions of non-weakly regular bent functions, and show the normality of the famous Coulter-Matthews bent function.