Idempotent and p-potent quadratic functions: Distribution of nonlinearity and co-dimension

Nurdagül Anbar, Wilfried Meidl, Alev Topuzoglu

The Walsh transform $\hat{Q}$ of a quadratic function $Q:F_{p^n}\to F_p$ satisfies $|\hat{Q}(b)|\in \{0,p^{\frac{n+s}{2}}\}$ for all $b\in F_{p^n}$, where $0\le s\…