2 problems

Let $m$ and $n$ be the parameters of the vectorial function $F$ under consideration, and let $u$ satisfy … with $u\not\equiv 2^k\pmod{2^m-1}$ for every $k\geq 0$. Define … where…

Let $m=2t$, let ${\mathbb F}$ be the finite field of size $2^m$, and let ${\mathcal C}_d$ be the binary cyclic code of length $2^m-1$ and dimension $2m$ with two nonzeros…