More on Quadratic functions and maximal Artin-Schreier curves

Nurdagül Anbar; Wilfried x Wilfried Meidl

doi:10.1007/s00200-015-0259-2

More on Quadratic functions and maximal Artin-Schreier curves

Nurdagül Anbar, Wilfried x Wilfried Meidl

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)>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. 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.

Original language	English
Journal	Applicable Algebra in Engineering, Communication and Computing
Volume	26
Issue number	5
Pages (from-to)	409-426
ISSN	0938-1279
DOIs	https://doi.org/10.1007/s00200-015-0259-2
Publication status	Published - 2015
Externally published	Yes

Keywords

Artin–Schreier curve
Partially bent function
Quadratic function
Walsh transform

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10.1007/s00200-015-0259-2

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

abstract = "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. 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.",

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T1 - More on Quadratic functions and maximal Artin-Schreier curves

AU - Anbar, Nurdagül

AU - Wilfried Meidl, Wilfried x

PY - 2015

Y1 - 2015

N2 - 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. 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.

AB - 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. 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.

KW - Artin–Schreier curve

KW - Partially bent function

KW - Quadratic function

KW - Walsh transform

U2 - 10.1007/s00200-015-0259-2

DO - 10.1007/s00200-015-0259-2

M3 - Journal article

SN - 0938-1279

VL - 26

SP - 409

EP - 426

JO - Applicable Algebra in Engineering, Communication and Computing

JF - Applicable Algebra in Engineering, Communication and Computing

IS - 5

ER -

More on Quadratic functions and maximal Artin-Schreier curves

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Keywords

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