Maiorana-McFarland type functions over the Galois ring GR(p~2, m)

摘要

Maiorana-McFarland functions defined over the binary field have been studied by several authors. These functions are related to various objects in Discrete Mathematics including bent functions and difference sets. In this note a class of functions defined over the Galois ring GR(p~2, m), where p is a prime and m a positive integer, which have similar properties as the binary Maiorana-McFarland functions are discussed. In the case where p = 2, results related to the Maiorana-McFarland functions given in [12] are recovered from those presented here.