Combinatorial t -designs from special functions

摘要

A special function is a function either of special form or with a special property. Special functions have interesting applications in coding theory and combinatorialt-designs. The main objective of this paper is to surveyt-designs constructed from special functions, including quadratic functions, almost perfect nonlinear functions, almost bent functions, bent functions, bent vectorial functions, and planar functions. These combinatorial designs are not constructed directly from such functions, but come from linear codes which are constructed with such functions. As a byproduct, this paper also surveys linear codes from certain special functions.