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

Sugata Gangopadhyay, Anand Joshi, Gregor Leander, Rajendra Kumar Sharma

Designs, Codes and Cryptography January 2013, Volume 66, Issue 1-3, pp 243-256


Abstract

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_ap type bents. It is also shown that all bent functions on 6 variables, up to equivalence, can be obtained by our construction.

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Tags: 06E30, 94C10, Boolean functions, Fourier transform, Z-bent functions