Finite length sequences with large nonlinear complexity

Abstract

Finite length sequences with large nonlinear complexity over $\mathbb{Z}_{p}\, (p≥ 2)$ are investigated in this paper. We characterize all $p$-ary sequences of length $n$ having nonlinear complexity $n-j$ for $j=2, 3$, where $n$ is an integer satisfying $n≥ 2j$. For $n≥ 8$, all binary sequences of length $n$ with nonlinear complexity $n-4$ are obtained. Furthermore, the numbers and $k$-error nonlinear complexity of these sequences are completely determined, respectively.