Walsh transforms of trace forms with three or more terms and some maximal Artin-Schreier curves

Abstract

We introduce some results for the Walsh transforms of quadratic trace forms with three or more terms. We also generalize some results on Kasami--Welch functions. We use Walsh transforms to obtain the number of rational points on Artin--Schreier curves over $\mathbb{F}_{2^k}.$ Later we construct some maximal Artin--Schreier curves over $\mathbb{F}_{2^k}$ for an even integer $k$.