Planar functions are functions over a finite field that have optimal combinatorial properties
and they have applications in several branches of mathematics, including algebra …

We describe how any function over a finite field $\mathbb {F} _ {p^ n} $ can be represented
in terms of the values of its derivatives. In particular, we observe that a function of algebraic …

Yu et al. described an algorithm for conducting computational searches for quadratic APN
functions over the finite field $\mathbb {F} _ {2^ n} $, and used this algorithm to give a …

Planar functions are mappings over a finite field Fpn having the best possible differential
uniformity. The differential uniformity is a measurement of the resistance of a function to …

Let $ p $ be a prime and $ n $ a positive integer. We present a deterministic algorithm for
deciding whether the matrix algebra $\mathbb {F} _p [A_1,\dots, A_t] $ with $ A_1,\dots …

In this thesis, we investigate the possibility of finding new planar functions and
corresponding semifields in characteristic 3 by the construction of isotopic semifields from …