Bent Vectorial Functions, Codes and Designs

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (GF(2
^2m
), +), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold 2-designs. A new coding-theoretic characterization of bent vectorial functions is presented.