On the Number of A ne Equivalence Classes of vectorial Boolean functions and q-Ary Functions

摘要

Vectorial Boolean functions play an important role in cryptography,sequences and coding theory. Both a ne equivalence and EA-equivalenceare well known equivalence relations between vectorial Boolean functions.In this paper, we give an exact formula for the number of a ne equivalenceclasses, and an asymptotic formula for the number of EA-equivalenceclasses of vectorial Boolean functions.