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Low dimensional lattices have a strict Voronoï basis

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

Andrew J. Mayer
Andrew J. Mayer
Affiliation:
Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, U.S.A.
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Abstract

We prove a generalization of a theorem of Ryshkov relating the Voronoï vectors of lattices to the defining conditions for the Minkowski fundamental domain . This is then used to prove that a Minkowski reduced basis of a lattice of dimension n < 7 consists of strict Voronoï vectors.

MSC classification

Secondary: 11H55: Quadratic forms (reduction theory, extreme forms, etc.)
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 229 - 238
Copyright
Copyright © University College London 1995

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