A Note on Partial Spread Generalized Bent Functions

Abstract

In this paper, we give a necessary and sufficient condition for a function with the form $tr(\sum _{i=1}^q{a}_i{x}^{i(q-1)})$ to be a generalized bent function. We indicate that these generalized bent functions are just those which could be constructed from partial spreads. We also introduce a method to calculate these generalized bent functions by means of interpolation.