Free Access
Volume 13, January 2009
Page(s) 437 - 458
Published online 22 September 2009
  1. J. Abbott and T. Mulders, How tight is Hadamard bound? Experiment. Math. 10 (2001) 331–336. [MathSciNet] [Google Scholar]
  2. A. Akhavi, Analyse comparative d'algorithmes de réduction sur les réseaux aléatoires. Ph.D. thesis, Université de Caen (1999). [Google Scholar]
  3. A. Akhavi, Random lattices, threshold phenomena and efficient reduction algorithms. Theor. Comput. Sci. 287 (2002) 359–385. [CrossRef] [Google Scholar]
  4. A. Akhavi, J.-F. Marckert and A. Rouault. On the reduction of a random basis, in D. Applegate, G.S. Brodal, D. Panario and R. Sedgewick Eds. Proceedings of the ninth workshop on algorithm engineering and experiments and the fourth workshop on analytic algorithmics and combinatorics. New Orleans (2007). [Google Scholar]
  5. T.W. Anderson, An introduction to multivariate statistical analysis. Wiley Series in Probability and Statistics, Third edition. John Wiley (2003). [Google Scholar]
  6. N.R. Chaganthy, Large deviations for joint distributions and statistical applications. Sankhya 59 (1997) 147–166. [Google Scholar]
  7. L. Chaumont and M. Yor, Exercises in probability. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (2003). [Google Scholar]
  8. H. Daudé and B. Vallée, An upper bound on the average number of iterations of the LLL algorithm. Theor. Comput. Sci. 123 (1994) 95–115. [CrossRef] [Google Scholar]
  9. J.D. Dixon, How good is Hadamard's inequality for determinants? Can. Math. Bull. 27 (1984) 260–264. [CrossRef] [Google Scholar]
  10. J.L. Donaldson, Minkowski reduction of integral matrices. Math. Comput. 33 (1979) 201–216. [CrossRef] [Google Scholar]
  11. A. Edelman and N.R. Rao, Random matrix theory. Acta Numerica (2005) 1–65. [Google Scholar]
  12. Y.H. Gan, C. Ling, and W.H. Mow, Complex Lattice Reduction Algorithm for Low-Complexity MIMO Detection. IEEE Trans. Signal Processing 57 (2009) 2701–2710. [CrossRef] [Google Scholar]
  13. J. Hadamard, Résolution d'une question relative aux déterminants. Bull. Sci. Math. 17 (1893) 240–246. [Google Scholar]
  14. R. Kannan, Algorithmic geometry of numbers, in Annual review of computer science, Vol. 2. Annual Reviews, Palo Alto, CA (1987) 231–267. [Google Scholar]
  15. D.E. Knuth, The art of computer programming, Vol. 2. Addison-Wesley Publishing Co., Reading, Mass., second edition. Seminumerical algorithms, Addison-Wesley Series in Computer Science and Information Processing (1981). [Google Scholar]
  16. H. Koy and C.P. Schnorr, Segment LLL-Reduction of Lattice Bases. Lect. Notes Comput. Sci. 2146 (2001) 67. [CrossRef] [Google Scholar]
  17. H.W. Lenstra Jr., Integer programming and cryptography. Math. Intelligencer 6 (1984) 14–19. [CrossRef] [MathSciNet] [Google Scholar]
  18. H.W. Lenstra Jr., Flags and lattice basis reduction. In European Congress of Mathematics, Vol. I (Barcelona, 2000). Progr. Math. 201 37–51. Birkhäuser, Basel (2001). [Google Scholar]
  19. A.K. Lenstra, H.W. Lenstra Jr. and L. Lovász, Factoring polynomials with rational coefficients. Math. Ann. 261 (1982) 515–534. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Letac, Isotropy and sphericity: some characterisations of the normal distribution. Ann. Statist. 9 (1981) 408–417. [CrossRef] [MathSciNet] [Google Scholar]
  21. R.J. Muirhead, Aspects of multivariate statistical theory. John Wiley (1982). [Google Scholar]
  22. H. Napias, A generalization of the LLL-algorithm over euclidean rings or orders. Journal de théorie des nombres de Bordeaux 8 (1996) 387–396. [Google Scholar]
  23. P.Q. Nguyen and J. Stern, The two faces of lattices in cryptology. In Cryptography and lattices (Providence, RI, 2001). Lect. Notes Comput. Sci. 2146 (2001) 146–180. Springer. [CrossRef] [Google Scholar]
  24. A. Rouault, Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles. ALEA Lat. Am. J. Probab. Math. Stat. 3 (2007) 181–230 (electronic). [MathSciNet] [Google Scholar]
  25. C.P. Schnorr, A hierarchy of polynomial time basis reduction algorithms. Theory of algorithms, Colloq. Pécs/Hung, 1984. Colloq. Math. Soc. János Bolyai 44 (1986) 375–386. [Google Scholar]
  26. B. Vallée, Un problème central en géométrie algorithmique des nombres : la réduction des réseaux. Autour de l'algorithme de Lenstra Lenstra Lovasz. RAIRO Inform. Théor. Appl. 3 (1989) 345–376. English translation by E. Kranakis in CWI-Quarterly - 1990 - 3. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.