How to calculate shortest vectors in a lattice
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- by U. Dieter PDF
- Math. Comp. 29 (1975), 827-833 Request permission
Abstract:
A method for calculating vectors of smallest norm in a given lattice is outlined. The norm is defined by means of a convex, compact, and symmetric subset of the given space. The main tool is the systematic use of the dual lattice. The method generalizes an algorithm presented by Coveyou and MacPherson, and improved by Knuth, for the determination of vectors of smallest Euclidean norm.References
- R. R. Coveyou and R. D. Macpherson, Fourier analysis of uniform random number generators, J. Assoc. Comput. Mach. 14 (1967), 100–119. MR 221727, DOI 10.1145/321371.321379 U. DIETER & J. H. AHRENS, Pseudo-Random Numbers, Preliminary version in preprint (430 pages), Wiley, New York. (To appear.)
- Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0286318
- George Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 25–28. MR 235695, DOI 10.1073/pnas.61.1.25 H. MINKOWSKI, Gesammelte Abhandlungen, especially Vol. I, pp. 243-260, Vol. II, pp. 3-42, Teubner-Verlag, Leipzig, 1911.
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 827-833
- MSC: Primary 10E20; Secondary 65K05
- DOI: https://doi.org/10.1090/S0025-5718-1975-0379386-6
- MathSciNet review: 0379386