Quadratic functions and maximal Artin–Schreier curves

For an odd prime p and an even integer n   with gcd⁡(n,p)=1gcd⁡(n,p)=1, we consider quadratic functions from FpnFpn to FpFp of codimension k. For various values of k  , we obtain classes of quadratic functions giving rise to maximal and minimal Artin–Schreier curves over FpnFpn. We completely classify all maximal and minimal curves obtained from quadratic functions of codimension 2 and coefficients in the prime field FpFp.