Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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
Posted: September 12, 2011
Supplement 1: Explanation of supplementary material
Supplement 2: Appendix
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\Lambda$ be a lattice in an -dimensional Euclidean space 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 , where $d\mathbb{Z}$ is the annihilator of $\Lambda/\Lambda'$ .

References

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Additional Information

Wolfgang Keller
Affiliation: Faculty of Mathematics, Otto-von-Guericke Universität, 39106 Magdeburg, Germany
Email: Wolfgang.Keller@student.uni-magdeburg.de

Jacques Martinet
Affiliation: Institut de Mathématiques, 351, cours de la Libération, 33405 Talence cedex, France
Email: Jacques.Martinet@math.u-bordeaux1.fr

Achill Schürmann
Affiliation: Institute of Mathematics, University of Rostock, 18051 Rostock, Germany
Email: achill.schuermann@uni-rostock.de

Mathieu Dutour Sikirić
Affiliation: Rudjer Bosković Institute, Bijenicka 54, 10000 Zagreb, Croatia
Email: mdsikir@irb.hr

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02528-7
PII: S 0025-5718(2011)02528-7
Keywords: Euclidean lattices, quadratic forms, linear codes
Received by editor(s): April 20, 2009
Received by editor(s) in revised form: January 29, 2011
Posted: 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 after 28 years from publication.

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