Estimates of lengths of shortest nonzero vectors in some lattices, II
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Alexander S. Rybakov
Abstract
In 1988, Friese et al. put forward lower estimates for the lengths of shortest nonzero vectors for “almost all” lattices of some families in the dimension 3. In 2004, the author of the present paper obtained a similar result for the dimension 4. Here by means of results obtained in part of the paper we show that these estimates also hold in the dimension 5.
Note
Originally published in Diskretnaya Matematika (2021) 33,№2, 117–140 (in Russian).
References
[1] Cassels J.W.S., An Introduction to the Geometry of Numbers, Springer-Verlag, 1959.10.1007/978-3-642-62035-5Suche in Google Scholar
[2] Prachar K., Primzahlverteilung, Springer-Verlag, Berlin Göttingen Heidelberg, 1957.Suche in Google Scholar
[3] Rybakov A.S., “The shortest vectors of lattices connected with a linear congruent generator”, Discrete Math. Appl., 14:5 (2004), 479–500.10.1515/1569392042572203Suche in Google Scholar
[4] Rybakov A.S., “Estimates of lengths of shortest nonzero vectors in some lattices, I”, Discrete Math. Appl., 33:1 (2021), 31–46.10.1515/dma-2022-0018Suche in Google Scholar
[5] Fel’dman N.I., Hilbert’s seventh problem, MSU, 1982 (in Russian), 312 pp.Suche in Google Scholar
[6] Friese A.M., Hastad J., Kannan R., Lagarias J.C., Shamir A., “Reconstructing truncated integer variables satisfying linear congruences”, SIAM J. Comput., 17:2 (1988), 262–28010.1137/0217016Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Contents
- Classification of Hadamard products of one-codimensional subcodes of Reed–Muller codes
- Asymptotical local probabilities of lower deviations for branching process in random environment with geometric distributions of descendants
- On the “tree” structure of natural numbers
- Estimates of lengths of shortest nonzero vectors in some lattices, II
- Curvature of the Boolean majority function
- Properties of proper families of Boolean functions
Artikel in diesem Heft
- Contents
- Classification of Hadamard products of one-codimensional subcodes of Reed–Muller codes
- Asymptotical local probabilities of lower deviations for branching process in random environment with geometric distributions of descendants
- On the “tree” structure of natural numbers
- Estimates of lengths of shortest nonzero vectors in some lattices, II
- Curvature of the Boolean majority function
- Properties of proper families of Boolean functions
