Generalization of some results on Gold and Kasami–Welch functions

We use some recent results of Fitzgerald (2009) [1], on quadratic functions with two trace terms in characteristic 2 to generalize some results of Lahtonen, McGuire and Ward (2007) [3], on Gold and Kasami–Welch functions. Then we get the Walsh spectrum of Q(x)=Tr(x2a+1+x2b+1) under certain conditions introduced in Lahtonen et al. (2007) [3] and finally introduce some new results on Gold and Kasami–Welch functions when the degree of extension is even.