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Search: id:A102780
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| A102780 |
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Ground states of the Bernasconi model. |
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+0
1
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| 0, 1, 1, 2, 2, 7, 3, 8, 12, 13, 5, 10, 6, 19, 15, 24, 32, 25, 29, 26, 26, 39, 47, 36, 36, 45, 37, 50, 62, 59, 67, 64, 64, 65, 73, 82, 86, 87, 99, 108, 108, 101, 109, 122, 118, 131, 135, 140, 136, 153, 153, 166, 170, 175, 171, 192, 188, 197, 205, 218
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Binary sequences of +1 and -1 with low autocorrelations have many applications in communication engineering. Their construction has a long tradition and has turned out to be a very hard mathematical problem. This problem is also called the low autocorrelation binary sequences (LABS) problem.
Bernasconi introduced an Ising spin model that allows one to formulate the construction problem in the framework of statistical mechanics.
Consider a sequence of binary variables or Ising spins of length N: S=(s_1, s_2, ..., s_N) s_i in {-1, +1} and their autocorrelations C_g = sum_{i=1..n-g} s_i s_{i + g}.
Bernasconi defined a Hamiltonian H(S) by H(S) = sum_{g = 1..N-1} (C_g)^2. The ground states (that minimize H(S)) of this model are the low autocorrelation binary sequences we are looking for.
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REFERENCES
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J. Bernasconi. Low autocorrelation binary sequences: statistical mechanics and configuration space analysis. J. Physique, 48:559, 1987.
M. J. E. Golay. The merit factor of long low autocorrelation binary sequences. IEEE Trans. Inform. Theory, IT-28:543, 1982.
Stephan Mertens. Exhaustive search for low-autocorrelation binary sequences. J. Phys. A, 29:L473-L481, 1996.
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LINKS
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Heiko Bauke, The Bernasconi Model.
Joshua Knauer, Merit Factor Records.
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CROSSREFS
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Sequence in context: A089588 A014840 A077218 this_sequence A115025 A075428 A116077
Adjacent sequences: A102777 A102778 A102779 this_sequence A102781 A102782 A102783
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KEYWORD
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nonn
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AUTHOR
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Heiko Bauke (heiko.bauke(AT)physik.uni-magdeburg.de), Feb 11 2005
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