Title :
A Counterexample to a Conjecture of Niho
Author :
Langevin, Philippe ; Leander, Gregor ; McGuire, Gary
Author_Institution :
GRIM-USTV, Univ. of Toulon, La Garde
Abstract :
A conjecture of Niho states that under certain assumptions the Fourier transform of the function Tr (xd) on F2n ,where d = (2tk1) /(2k +1), has a spectrum with at most five values. We present a counterexample to this conjecture, and the theory behind finding it. We use the theory of quadratic forms over F2.
Keywords :
Fourier transforms; Walsh functions; Fourier transform; Niho states conjecture; quadratic forms theory; spectrum; Boolean functions; Fourier transforms; Galois fields; Gold; Polarization; Terminology; 5-valued; Fourier; Walsh; quadratic form; spectrum;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.909109
