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 Fpn to Fp of codimension k. For various values of k, we obtain classes of quadratic functions giving rise to maximal and minimal Artin–Schreier curves over Fpn. We completely classify all maximal and mini...

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Bibliographic Details
Published in:Finite fields and their applications 2014-11, Vol.30, p.49-71
Main Authors: Anbar, Nurdagül, Meidl, Wilfried
Format: Article
Language:English
Subjects:
Artin–Schreier curve
Partially bent function
Quadratic function
Walsh transform
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Summary:For an odd prime p and an even integer n with gcd⁡(n,p)=1, we consider quadratic functions from Fpn to Fp of codimension k. For various values of k, we obtain classes of quadratic functions giving rise to maximal and minimal Artin–Schreier curves over Fpn. We completely classify all maximal and minimal curves obtained from quadratic functions of codimension 2 and coefficients in the prime field Fp.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2014.05.008