English

Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field

Information Theory 2022-10-07 v2 math.IT

Abstract

For r1r \geq 1 an odd integer, we provide a sequence from the function field Fq,r\mathcal{F}_{q, r} of the maximal curve over Fq2r\mathbb{F}_{q^{2r}} defined by the affine equation yq+y=xqr+1y^q+y=x^{q^r + 1}. This sequence has high nonlinear complexity, and this fact comes from the existence of a rational function on Fq,r\mathcal{F}_{q, r} with pole divisor of small degree, and support in certain qq rational places.

Cite

@article{arxiv.1909.08061,
  title  = {Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field},
  author = {Alonso S. Castellanos and Luciane Quoos and Guilherme Tizziotti},
  journal= {arXiv preprint arXiv:1909.08061},
  year   = {2022}
}
R2 v1 2026-06-23T11:18:27.910Z