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Automorphisms and equivalence of bent functions and of difference sets in elementary abelian 2-groups. (English) Zbl 1085.05019
Summary: 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.

MSC:
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
51D20 Combinatorial geometries and geometric closure systems
20J06 Cohomology of groups
68R99 Discrete mathematics in relation to computer science
94B25 Combinatorial codes
Software:
GAP
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