Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Hans Olav Geil; Ferruh Ozbudak; Diego Ruano Benito

doi:10.1007/s00233-018-9976-8

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Hans Olav Geil, Ferruh Ozbudak, Diego Ruano Benito

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Abstract

Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.

Original language	English
Journal	Semigroup Forum
Volume	98
Pages (from-to)	543-555
Number of pages	13
ISSN	0037-1912
DOIs	https://doi.org/10.1007/s00233-018-9976-8
Publication status	Published - 2019

Keywords

Weierstrass semigroup
Weierstrass pair
Hermitian function field
Sequences
Nonlinear complexity

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10.1007/s00233-018-9976-8

SF2018eprintAccepted author manuscript, 347 KBLicence: CC BY-NC-ND 4.0

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AU - Ruano Benito, Diego

PY - 2019

Y1 - 2019

N2 - Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.

AB - Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.

KW - Weierstrass semigroup

KW - Weierstrass pair

KW - Hermitian function field

KW - Sequences

KW - Nonlinear complexity

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U2 - 10.1007/s00233-018-9976-8

DO - 10.1007/s00233-018-9976-8

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JO - Semigroup Forum

JF - Semigroup Forum

ER -

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

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