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

摘要

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.