Exhaustive search for low autocorrelation binary sequences

Details Exhaustive search for low autocorrelation binary sequences Exhaustive search for low autocorrelation binary sequences

1996-05-08

arxiv.org/abs/cond-mat/9605050v2

Physics

Condensed Matter

6 pages, LaTeX2e, several packages, 3 figures (eps), extended version contains data for N=47 and 48

Scientific paper

10.1088/0305-4470/29/18/005

Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the exponential size $O(2^N)$ of the configuration space, exhaustive searches are limited to short sequences. We discuss an exhaustive search algorithm with run time characteristic $O(1.85^N)$ and apply it to compile a table of exact groundstates of the Bernasconi-model up to $N=48$. The data suggests $F>9$ for the optimal merit factor in the limit $N\to\infty$.

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