Low Autocorrelation Binary Sequences

Abstract

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 $\Theta(N\,1.73^N)$. We computed all optimal sequences for $N\leq 66$ and all optimal skewsymmetric sequences for $N\leq 119$.