A new construction of bent functions based on $${\mathbb{Z}}$$ -bent functions

Abstract

Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called $${\mathbb{Z}}$$ -bent functions. Following his ideas, we generalize the construction of partial spreads bent functions to partial spreads $${\mathbb{Z}}$$ -bent functions of arbitrary level. Furthermore, we show how these partial spreads $${\mathbb{Z}}$$ -bent functions give rise to a new construction of (classical) bent functions. Further, we construct a bent function on 8 variables which is inequivalent to all Maiorana---McFarland as well as PS ap type bents. It is also shown that all bent functions on 6 variables, up to equivalence, can be obtained by our construction.