# Low Autocorrelation Binary Sequences

arXiv: https://arxiv.org/abs/1512.02475 · HTML: https://mlsanity.com/paper/1512.02475/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2015.

## Built on by (most cited first, 11 of 11)

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- [Reconstructing Rational Functions on Finite Abelian Groups with Higher Autocorrelations](https://mlsanity.com/paper/2503.21022/) (2025)
- [MOCA-HESP: Meta High-dimensional Bayesian Optimization for Combinatorial and Mixed Spaces via Hyper-ellipsoid Partitioning](https://mlsanity.com/paper/2508.06847/) (2025)
- [Prioritizing Search Space Regions in the Low Autocorrelation Binary Sequences Problem](https://mlsanity.com/paper/2607.09688/) (2026)
- [ILP-BO: Integer Linear Programming-Based Black-Box Optimization](https://mlsanity.com/paper/2609.33131/) (2026)
- [EvoDuet: Bilevel Co-Evolution of Web Searching and Task Solving for Scientific Discovery](https://mlsanity.com/paper/2609.40340/) (2026)

## Abstract (arXiv)

Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a notoriously hard problem, that so far can be solved only by exhaustive search. We review recent algorithms and present a new algorithm that finds optimal sequences of length N in time Theta(N,1.73N). We computed all optimal sequences for N≤ 66 and all optimal skewsymmetric sequences for N≤ 119.