A Counterexample to a Conjecture of Niho

A conjecture of Niho states that under certain assumptions the Fourier transform of the function Tr (x d ) on F 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...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	IEEE transactions on information theory 2007-12, Vol.53 (12), p.4785-4786
Hauptverfasser:	Langevin, P., Leander, G., McGuire, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	5-valued Applied sciences Boolean functions Computer Science Discrete Mathematics Electronics Exact sciences and technology Fourier Fourier transforms Galois fields Gold Information theory Information, signal and communications theory Polarization quadratic form Quadratic forms Quadratic programming spectrum Telecommunications and information theory Terminology Theory Walsh
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	A conjecture of Niho states that under certain assumptions the Fourier transform of the function Tr (x d ) on F 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 F 2 .
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2007.909109