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arXiv · 1512.02475

Low Autocorrelation Binary Sequences

Tom Packebusch·Stephan Mertens
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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 $N\leq 119$.

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Tom Packebusch, Stephan Mertens. 2015-12-08. Low Autocorrelation Binary Sequences. https://doi.org/10.1088/1751-8113/49/16/165001

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