Further results on autocorrelation of vectorial Boolean functions

In this paper, we study the properties of sum-of-squares indicator vectorial Boolean functions. Firstly, give upper bound $\sum_{u\in \mathbb{F}_2^n,v\in \mathbb{F}_2^m}\mathcal{W}_F^3(u,v)$. Secondly, based on Walsh-Hadamard transform, a secondary construction bent Further, three kinds indicators functions are defined by autocorrelation function and lower bounds derived. Finally, with respect to several equivalence relations, get which have best cryptographic properties.