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On classifying Minkowskian sublattices

Authors: Wolfgang Keller, Jacques Martinet and Achill Schürmann; with an Appendix by Mathieu Dutour Sikirić
Journal: Math. Comp. 81 (2012), 1063-1092
MSC (2010): Primary 11H55, 11H71
Published electronically: September 12, 2011
Supplement 1: Explanation of supplementary material
Supplement 2: Appendix
MathSciNet review: 2869050
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Abstract: Let $ \Lambda$ be a lattice in an $ n$-dimensional Euclidean space $ E$ and let $ \Lambda'$ be a Minkowskian sublattice of $ \Lambda$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $ \Lambda$. We extend the classification of possible $ \mathbb{Z}/d\mathbb{Z}$-codes of the quotients $ \Lambda/\Lambda'$ to dimension $ 9$, where $ d\mathbb{Z}$ is the annihilator of $ \Lambda/\Lambda'$.

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Additional Information

Wolfgang Keller
Affiliation: Faculty of Mathematics, Otto-von-Guericke Universität, 39106 Magdeburg, Germany

Jacques Martinet
Affiliation: Institut de Mathématiques, 351, cours de la Libération, 33405 Talence cedex, France

Achill Schürmann
Affiliation: Institute of Mathematics, University of Rostock, 18051 Rostock, Germany

Mathieu Dutour Sikirić
Affiliation: Rudjer Bosković Institute, Bijenicka 54, 10000 Zagreb, Croatia

Keywords: Euclidean lattices, quadratic forms, linear codes
Received by editor(s): April 20, 2009
Received by editor(s) in revised form: January 29, 2011
Published electronically: September 12, 2011
Additional Notes: The first and the third authors were supported by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-2. The third author was additionally supported by the Université Bordeaux 1
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.