Bent functions and strongly regular graphs

The family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on ${\mathbb{Z}}_2^n$ by the support of a bent function is a strongly regular graph $srg(v,k\lambda ,\mu )$, with $\lambda =\mu$. In this note we list the parameters of such Cayley graphs. Moreover, it is given a condition on $(n,m)$-bent functions $F=(f_1,\dots ,f_m)$, involving the support of their components $f_i$, and their $n$-ary symmetric differences.