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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Improved methods for calculating vectors of short length in a lattice, including a complexity analysis
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by U. Fincke and M. Pohst PDF
Math. Comp. 44 (1985), 463-471 Request permission

Abstract:

The standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of ${{\mathbf {Z}}^m}$ in a suitable box. However, it suffices to consider those ${\mathbf {x}} \in {{\mathbf {Z}}^m}$ which lie in a suitable ellipsoid having a much smaller volume than the box. We show in this paper that searching through that ellipsoid is in many cases much more efficient. If combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions. Several randomly constructed numerical examples illustrate the superiority of our new method over the known ones.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 463-471
  • MSC: Primary 11H50; Secondary 11H55
  • DOI: https://doi.org/10.1090/S0025-5718-1985-0777278-8
  • MathSciNet review: 777278