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

  • Olav Geil
  • Ferruh Özbudak
  • Diego Ruano
Research Article


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.


Weierstrass semigroup Weierstrass pair Hermitian function field Sequences Nonlinear complexity 



The authors are grateful to Department of Mathematical Sciences, Aalborg University for supporting a one month visiting professor position for the second listed author. This work was supported by The Danish Council for Independent Research (Grant No. DFF–4002-00367), by the Spanish MINECO/FEDER (Grant No. MTM2015-65764-C3-2-P, MTM2015-69138-REDT and RYC-2016-20208 (AEI/FSE/UE)) and by METU Coordinatorship of Scientific Research Projects via grant for projects BAP-01-01-2016-008 and BAP-07-05-2017-007.


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Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematics, Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.IMUVA (Mathematics Research Institute)University of ValladolidValladolidSpain

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