This paper examines a pair of bent functions on Z 2 and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph whose colours are defined by the properties of a canonical basis for the real representation of the Clifford algebra Rm,m. Some other necessary conditions are also briefly examined.

A notion of the graph of minimal distances of bent functions is introduced. It is an undirected graph (V , E) where V is the set of all bent functions in 2k variables and (f, g) ∈ E if the Hamming distance between f and g is equal to 2 (it is the minimal possible distance between two different bent functions). The maximum degree of the graph is obtained and it is shown that all its vertices of ...

In this paper we consider cubic bent functions obtained by Leander and McGuire (J. Comb. Th. Series A, 116 (2009) 960-970) which are concatenations of quadratic Gold functions. A lower bound of second-order nonlinearities of these functions is obtained. This bound is compared with the lower bounds of second-order nonlinearities obtained for functions belonging to some other classes of functions...

This note is a response to a request by Claude Carlet for a brief summary of some of what is known about spreads for use in John Dillon’s fundamental partial spread construction of bent functions. This note was not written to be published.

We present a construction of bent function fa,S with n = 2m variables for any nonzero vector a ∈ F2 and subset S of F2 satisfying a + S = S. We give the simple expression of the dual bent function of fa,S . We prove that fa,S has optimal algebraic degree m if and only if |S| ≡ 2(mod4). This construction provides series of bent functions with optimal algebraic degree and large symmetric group if...