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

Abstract

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

Cited by in corpus (1)

• Weierstrass Semigroup, Pure Gaps and Codes on Function Fields