On Minimal Distance between q-ary Plateaued Functions

摘要

It is proved that the Hamming distance between distinct binary s-plateaued functions of n variables is not less than $2^{frac{s + n - 2}{2}}$ and the Hamming distance between distinct ternary s-plateaued functions of n variables is not less than $3^{frac{s + n - 1}{2}}$. It is shown that this bound is tight. Constructions and some properties of q-ary plateaued functions are discussed.