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.

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