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Mathematics of Computation

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How to calculate shortest vectors in a lattice


Author: U. Dieter
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0379386-6
Keywords: Geometry of numbers, lattice theory, minima of forms, random number generation
Article copyright: © Copyright 1975 American Mathematical Society