# Dual-Step Optimization for Binary Sequences with High Merit Factors

arXiv: https://arxiv.org/abs/2409.07222 · HTML: https://mlsanity.com/paper/2409.07222/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Prioritizing Search Space Regions in the Low Autocorrelation Binary Sequences Problem](https://mlsanity.com/paper/2607.09688/) (2026)

## Abstract (arXiv)

The problem of finding aperiodic low auto-correlation binary sequences (LABS) presents a significant computational challenge, particularly as the sequence length increases. Such sequences have important applications in communication engineering, physics, chemistry, and cryptography. This paper introduces a novel dual-step algorithm for long binary sequences with high merit factors. The first step employs a parallel algorithm utilizing skew-symmetry and restriction classes to generate sequence candidates with merit factors above a predefined threshold. The second step uses a priority queue algorithm to refine these candidates further, searching the entire search space unrestrictedly. By combining GPU-based parallel computing and dual-step optimization, our approach has successfully identified new best-known binary sequences for all lengths ranging from 450 to 527, with the exception of length 518, where the previous best-known value was matched with a different sequence. This hybrid method significantly outperforms traditional exhaustive and stochastic search methods, offering an efficient solution for finding long sequences with good merit factors.