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 languageEnglish
JournalSemigroup Forum
Volume98
Pages (from-to)543-555
Number of pages13
ISSN0037-1912
DOIs
Publication statusPublished - 2019

Keywords

  • Weierstrass semigroup
  • Weierstrass pair
  • Hermitian function field
  • Sequences
  • Nonlinear complexity

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