Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation

Abstract

We prove a conjecture of Helleseth that claims that for any $n \geq 0$, a pair of binary maximal linear sequences of period $2^{2^n}-1$ can not have a three-valued cross-correlation function.