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 $N\leq 119$.