Low autocorrelation binary sequences
Tom Packebusch, Stephan Mertens · Journal of Physics A Mathematical and Theoretical · 2016
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 O ( N 1.73 N ) . We computed all optimal sequences for N ⩽ 66 and all optimal skewsymmetric sequences for N ⩽ 119 .