Rayleigh quotients of Dillon’s functions

Abstract

The Walsh-Hadamard spectrum of a bent function uniquely determines a dual function. The duality mapping is the only isometric mapping on the set of bent functions apart from its automorphisms that preserve bentness. The Hamming distance between a bent function and its dual is related to its Rayleigh quotient. In this paper, we study the Rayleigh quotient of a class of bent functions called Dillon’s functions. Carlet et al. [2] studied Rayleigh quotients of bent functions in , and Danielsen et al. [4] obtained an expression in terms of character sums. In this paper, we employ another approach comprising Desarguesian spreads to obtain the complete spectrum of Rayleigh quotients of bent functions in .