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


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Geil O., Ozbudak F., Ruano D.

SEMIGROUP FORUM, vol.98, no.3, pp.543-555, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1007/s00233-018-9976-8
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.543-555
  • Keywords: Weierstrass semigroup, Weierstrass pair, Hermitian function field, Sequences, Nonlinear complexity

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, Theorem3) considerably and the bound in Niederreiter and Xing (2014, Theorem4) for some parameters.