  In this paper, the construction of finite-length binary sequences whose
nonlinear complexity is not less than half of the length is investigated. By
characterizing the structure of the sequences, an algorithm is proposed to
generate all binary sequences with length $n$ and nonlinear complexity
$c_{n}\geq n/2$, where $n$ is an integer larger than $2$. Furthermore, a
formula is established to calculate the exact number of these sequences. The
distribution of nonlinear complexity for these sequences is thus completely
determined.
