Quadratic functions and maximal Artin-Schreier curves

Nurdagül Anbar; Wilfried Meidl

doi:10.1016/j.ffa.2014.05.008

Quadratic functions and maximal Artin-Schreier curves

Nurdagül Anbar, Wilfried Meidl

Sabanci University

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

For an odd prime p and an even integer n with gcd⁡(n,p)=1gcd⁡(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.

Original language	English
Journal	Finite Fields and Their Applications
Volume	30
Issue number	November
Pages (from-to)	49-71
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2014.05.008
Publication status	Published - 2014
Externally published	Yes

Keywords

Artin–Schreier curve
Partially bent function
Quadratic function
Walsh transform

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10.1016/j.ffa.2014.05.008

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title = "Quadratic functions and maximal Artin-Schreier curves",

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AU - Anbar, Nurdagül

AU - Meidl, Wilfried

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N2 - For an odd prime p and an even integer n with gcd⁡(n,p)=1gcd⁡(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.

AB - For an odd prime p and an even integer n with gcd⁡(n,p)=1gcd⁡(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.

KW - Artin–Schreier curve

KW - Partially bent function

KW - Quadratic function

KW - Walsh transform

U2 - 10.1016/j.ffa.2014.05.008

DO - 10.1016/j.ffa.2014.05.008

M3 - Journal article

SN - 1071-5797

VL - 30

SP - 49

EP - 71

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

IS - November

ER -

Quadratic functions and maximal Artin-Schreier curves

Abstract

Keywords

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