Further Investigations on Nonlinear Complexity of Periodic Binary Sequences

TL;DR

This paper explores how circular shifts influence the nonlinear complexity of finite binary sequences and introduces algorithms to generate all periodic sequences with a specified nonlinear complexity.

Contribution

It establishes a relation between nonlinear complexities of finite and periodic binary sequences and proposes algorithms for sequence generation based on this relation.

Findings

Circular shifts affect nonlinear complexity of binary sequences

A explicit relation between finite and periodic sequence complexities is revealed

Algorithms for generating sequences with prescribed nonlinear complexity are proposed

Abstract

Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit relation between nonlinear complexities of finite-length binary sequences and their corresponding periodic sequences. Based on the relation, we propose two algorithms that can generate all periodic binary sequences with any prescribed nonlinear complexity.