A Counterexample to a Conjecture of Niho
Philippe Langevin, Gregor Leander, Gary McGuire · IEEE Transactions on Information Theory · 2007
A conjecture of Niho states that under certain assumptions the Fourier transform of the function${\rm Tr}(x^{d})$on$\BBF _{2^{n}}$, where$d=(2^{tk}+1)/(2^{k}+1)$, 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$\BBF _{2}$.