A new class of semi-bent quadratic Boolean functions

In this paper, we present a new class of semi-bent quadratic Boolean functions of the form f(x) = ∑⌊m−1 2 ⌋ i=1 Tr n 1 (cix 1+4i) (ci ∈ F4,n = 2m). We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when m is odd. For the case: m = p, where p is an odd prime with some conditions, we enumerate the semi-bent functions. Further, we give a simple characterization of semi-bentness for these functions with linear properties of ci. In particular, for a special case of p, any quadratic Boolean function f(x) = ∑ p−1 2 i=1 Tr 2p 1 (cix 1+4i) over F22p is a semi-bent function.