A new construction of bent functions based on Z-bent functions

摘要

Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called Z-bent functions. Following his ideas, we generalize the construction of partial spreads bent functions to partial spreads Z-bent functions of arbitrary level. Furthermore, we show how these partial spreads 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_(qp) type bents. It is also shown that all bent functions on 6 variables, up to equivalence, can be obtained by our construction.