MAXIMAL SEQUENCES

Let ${\bf F}_q$ be a finite extension of ${\bf F}_2$.
Let $\alpha$ be a primitive root of ${\bf F}_q$.
    The binary sequence of period $q-1$,

$$s_i = \chi( {\rm tr}_{{L}/{{\bf F}_2}} ( \alpha^i) ) = \mu(\alpha^ i)$$

has small periodic autocorrelation.

    Indeed,

$$\begin{split}s\times s(\tau) &= \sum_{x\in{L}^\times} \mu(\a......v 0\mod (q-1)$ ;}\\-1,&\text{else.}\\\end{cases}\end{split}$$

    very algebraic !