How to calculate shortest vectors in a lattice-Reference-Cited by-同舟云学术

How to calculate shortest vectors in a lattice

Published:1975 Issue:131 Volume:29 Page:827-833
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Dieter U.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1975-29-131/S0025-5718-1975-0379386-6/S0025-5718-1975-0379386-6.pdf

Reference5 articles.

1. Fourier analysis of uniform random number generators;Coveyou, R. R.;J. Assoc. Comput. Mach.,1967

2. U. DIETER & J. H. AHRENS, Pseudo-Random Numbers, Preliminary version in preprint (430 pages), Wiley, New York. (To appear.)

3. Random numbers fall mainly in the planes;Marsaglia, George;Proc. Nat. Acad. Sci. U.S.A.,1968

4. H. MINKOWSKI, Gesammelte Abhandlungen, especially Vol. I, pp. 243-260, Vol. II, pp. 3-42, Teubner-Verlag, Leipzig, 1911.

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