Some properties of q-ary bent functions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).

Let F be a function from a finite field Q to a finite field P. Here, both fields are of characteristic 2, |P| = q ^ 2 and Q is the expansion of the field P. The period of F is defined as the period of the sequence u(i) = F(0 ) (0 - primitive element of Q, i G No). Besides, let N _a(F) be a number of solutions in Q of equation F(x) = а, а G P. Consider F to be a bent function. In this case, it is shown that if the period of F is not maximal one, then exact values of N _a(F), а G P, can be derived. Moreover, if values of N _a(F), а G P, are of a special form, then the value of the period of F is divisible by some exact value.