Calculation of Minkowski-reduced lattice bases

DOI10.1007/BF02240194zbMath0557.10025OpenAlexW1514236938MaRDI QIDQ762199

Lothar Afflerbach, Holger Grothe

Publication date: 1985

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02240194

zbMATH Keywords

algorithmrandom number generationlattice structurecomputational number theoryreduction of quadratic formsCholesky's methodgreater dimensionsMinkowski-reduced lattice bases

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Random number generation in numerical analysis (65C10) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Algorithms in computer science (68W99)

Related Items (12)

On the structure of quadratic congruential sequences ⋮ The sub-lattice structure of linear congruential random number generators ⋮ A statistical analysis of the screening measure of multiple recursive random number generators of orders one and two ⋮ The lattice structure of pseudo-random vectors generated by matrix generators ⋮ Several extensively tested multiple recursive random number generators ⋮ On the distribution of integration error by randomly-shifted lattice rules ⋮ Upper bounds for the Beyer ratios of linear congruential generators ⋮ Criteria for the assessment of random number generators ⋮ Upper bounds in spectral test for multiple recursive random number generators with missing terms ⋮ Geodesic continued fractions and LLL ⋮ Parallel Cholesky-based reduction for the weighted integer least squares problem ⋮ Uniform random number generation

Cites Work

• The sub-lattice structure of linear congruential random number generators
• Minkowskische Reduktionsbedingungen für positiv definite quadratische Formen in 5 Variablen
• The theory of Hermite-Minkowski reduction of positive definite quadratic forms
• The Hermite-Minkowski domain of reduction of positive definite quadratic forms in six variables
• Regularities in congruential random number generators
• On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications
• How to Calculate Shortest Vectors in a Lattice
• RANDOM NUMBERS FALL MAINLY IN THE PLANES
• The Lattice Structure of Multiplicative Congruential Pseudo-Random Vectors
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