Helleseth's conjecture on cross-correlation of maximal linear sequences

Let $m$ be a positive integer, let $\alpha$ generate $\operatorname{GF}(2^m)^*$, and let $d$ be an integer with $\gcd(d,2^m-1)=1$. Define

$$C_d(t)=\sum_{x\in\operatorname{GF}(2^m)^*}(-1)^{\operatorname{Tr}(\alpha^{-t}x+x^d)},$$

where $\operatorname{Tr}\colon\operatorname{GF}(2^m)\to\operatorname{GF}(2)$ is the absolute trace and $t\in\mathbb Z/(2^m-1)\mathbb Z$. A function $C_d(t)$ is three-valued if it takes exactly three distinct values as $t$ varies.

Helleseth's conjecture. If $m$ is a power of $2$, then $C_d(t)$ is not three-valued.

This conjecture concerns the cross-correlation of binary maximal linear recursive sequences. The paper proves the conjecture, so the assertion is no longer open.