# Maximum-order Complexity and Correlation Measures

## TL;DR

This paper investigates the relationship between the maximum-order complexity of binary sequences and their correlation measures, showing that low correlation measures up to a certain order imply a lower bound on complexity.

## Contribution

It establishes a new connection between correlation measures and maximum-order complexity, providing bounds that link sequence correlation properties to complexity measures.

## Key findings

- Sequences with small correlation measures up to order k cannot have very low maximum-order complexity.
- The paper provides bounds relating correlation measures to complexity, enhancing understanding of sequence unpredictability.
- The results have implications for analyzing the randomness and security of binary sequences.

## Abstract

We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small maximum-order complexity.