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Sieves for low autocorrelation binary sequences
Abstract
The value2e^{2}is calculated by approximations as a conjectured asymptotic limit for the best central to sidelobe energy ratio of very long low autocorrelation binary sequences. The same bound is calculated by approximation for skewsymmetric sequences, hence it is concluded that the requirement of skewsymmetry constitutes a powerful and effective sieve for the search for near-optimal sequences. A second sieve based on the use of complementary sequences is discussed and shown to be quite effective for sequence lengths up to 31, and its investigation for longer lengths by means of computers is suggested. A third and a fourth sieve, based on the selection of restricted classes of complementary sequences, are also discussed.
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Citations
Cited by
Optimization Methods for Designing Sequences With Low Autocorrelation Sidelobes
Song, J., Babu, P., & Palomar, D. P. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2425808 · Cited by 382
Shaydulin, R., Li, C., Chakrabarti, S., DeCross, M., Herman, D., Kumar, N., Larson, J., Lykov, D., Minssen, P., Sun, Y., et al. (2024) · Science Advances · doi:10.1126/sciadv.adm6761 · Cited by 120
“(14) In LABS, the energy E sidelobe ( s ) grows as N 2 , so γ ∗ decreases as 1 N .”
MethodFinding low autocorrelation binary sequences with memetic algorithms
Gallardo, J. E., Cotta, C., & Fernández, A. J. (2009) · Applied Soft Computing · doi:10.1016/j.asoc.2009.03.005 · Cited by 59
Bošković, B., Brglez, F., & Brest, J. (2017) · Applied Soft Computing · doi:10.1016/j.asoc.2017.02.024 · Cited by 31
Metadata
- Authors
- Golay, M.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1977-01
- Volume
- 23
- Issue
- 1
- Pages
- 43-51
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2123547620
- Cited by
- 225
- References
- 0
- FWCI
- 1.45
- Type
- journal article
- Language
- en
- Open access
- closed
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- Golay, M. (1977). Sieves for low autocorrelation binary sequences. IEEE Transactions on Information Theory. https://doi.org/10.1109/tit.1977.1055653
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