Homogeneous bent functions of degree n in 2n variables do not exist for n > 3

T. Xia, University of Wollongong
J. Seberry, University of Wollongong
J. Pieprzyk, Macquarie University
C. Charnes, University of Melbourne

Article comments

This article was originally published as Xia, T, Seberry, J, Pieprzyk, J and Charnes, C, Homogeneous bent functions of degree n in 2n variables do not exist for n > 3, Discrete Applied Mathematics, 142, 2004, 127-132. Original Elsevier journal available here.

Abstract

We prove that homogeneous bent functions f : GF(2)2n —> GF(2) of degree n do not exist for n > 3. Consequently homogeneous bent functions must have degree < n for n > 3.