Additive autocorrelation of some classes of cubic semi-bent Boolean functions

In this paper, we investigate the relation between the autocorrelation of a cubic Boolean function f\in \cB_n at a \in \BBF_{2^n} and the kernel of the bilinear form associated with $D_{a}f$, the derivative of $f$ at $a$. Further, we apply this technique to obtain the tight upper bounds of absolute indicator and sum-of-squares indicator for avalanche characteristics of various classes of highly nonlinear non-bent cubic Boolean functions