Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (\gf(22m),+), 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.
@article{arxiv.1808.08487,
title = {Bent Vectorial Functions, Codes and Designs},
author = {Cunsheng Ding and Akihiro Munemasa and Vladimir Tonchev},
journal= {arXiv preprint arXiv:1808.08487},
year = {2019}
}