Automorphisms and Equivalence of Bent Functions and of Difference Sets in Elementary Abelian 2-Groups

ABSTRACT

The problem of computing the automorphism groups of an elementary Abelian Hadamard difference set or equivalently of a bent function seems to have attracted not much interest so far. We describe some series of such sets and compute their automorphism group. For some of these sets the construction is based on the nonvanishing of the degree 1-cohomology of certain Chevalley groups in characteristic two. We also classify bent functions f such that Aut(f) together with the translations from the underlying vector space induce a rank 3 group of automorphisms of the associated symmetric design. Finally, we discuss computational aspects associated with such questions.

Key Words:

• Automorphism group
• Bent function
• Difference set

Mathematics Subject Classification:

• Primary 05B10, 20F32, 51D20
• Secondary 20J06, 68R99, 94B25

ACKNOWLEDGMENTS

I like to thank the persons who developed GAP. This package was essential for the computations of the previous section. It was also very useful for the theoretical results as computations in small cases often indicated a general statement.

Notes

Communicated by A. Turull.