2 research outputs found
On the conjecture about the nonexistence of rotation symmetric bent functions
In this paper, we describe a different approach to the proof of the
nonexistence of homogeneous rotation symmetric bent functions. As a result, we
obtain some new results which support the conjecture made in this journal,
i.e., there are no homogeneous rotation symmetric bent functions of degree >2.
Also we characterize homogeneous degree 2 rotation symmetric bent functions by
using GCD of polynomials
Rotation Symmetric Bent Boolean Functions for n = 2p
It has been conjectured that there are no homogeneous rotation symmetric bent
Boolean functions of degree greater than two. In this paper we begin by proving
that sums of short-cycle rotation symmetric bent Boolean functions must contain
a specific degree two monomial rotation symmetric Boolean function. We then
prove most cases of the conjecture in n=2p, p>2 prime, variables and extend
this work to the nonhomogeneous case.Comment: 16 page