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

The problem of computing the automorphism groups of elementary abelian Hadamard difference sets or equivalently of bent functions 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-chohomology 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. 1 Introduction. Let V = V (N, 2) be an N-dimensional GF(2)-space and B a subset of V. We assume that B + v � = B for 0 � = v ∈ V and set B = {B + v | v ∈ V}. If the incidence structure D(B) = (V, B) is a symmetric (2 N, k, λ)-design on

The translation planes of order 49 and their automorphism groups

Abstract. Using isomorphism invariants, we enumerate the translation planes of order 49 and determine their automorphism groups. 1

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the computer enumeration of bent functions by Meng et al

On 2-transitive sets of equiangular lines

http://dx.doi.org/10.1017/S000497271200033