More on 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-p(n) 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-p(n). We completely classify all maximal and minimal curves obtained from quadratic functions of codimension 2 and coefficients in the prime field F-p. The results complement our results obtained earlier for the case gcd( n, p) = 1. The arguments are more involved than for the case gcd( n, p) = 1.