Essential dependence of the Kasami bent functions on the products of variables

The Kasami bent functions are the most complicated of the class of monomial bent functions. It is proved that an arbitrary Kasami bent function of degree $t$ has nonzero $(t-2)$-multiple derivatives if $4\leq t\leq(n+3)/3$ and nonzero $(t-3)$-multiple derivatives if $(n+3)/3<t\leq n/2$. It is obtained that the order of essential dependence of a Kasami bent function is not less than $t-3$. Bibliogr. 8.