Quadratic functions and maximal Artin-Schreier curves

For an odd prime p and an even integer n with gcd(n,p) = 1, we consider quadratic functions from F-pn to F-p of codimension k. For various values of k, we obtain classes of quadratic functions giving rise to maximal and minimal Artin-Schreier curves over F-pn. We completely classify all maximal and minimal curves obtained from quadratic functions of codimension 2 and coefficients in the prime field F-p (C) 2014 Elsevier Inc. All rights reserved.