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

DOI:
https://doi.org/10.1090/S0025-5718-2011-02528-7

Published electronically:
September 12, 2011

Supplement 1:
Explanation of supplementary material

Supplement 2:
Appendix

MathSciNet review:
2869050

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a lattice in an -dimensional Euclidean space and let be a Minkowskian sublattice of , that is, a sublattice having a basis made of representatives for the Minkowski successive minima of . We extend the classification of possible -codes of the quotients to dimension , where is the annihilator of .

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SOFTWARE**[Convex]**, ver. 1.1.3, by Matthias Franz,`Convex`- a Maple package for convex geometry`http://www.math.uwo.ca/~mfranz/convex/`.**[lrs]**, ver. 4.2, by D. Avis,`lrs`- C implementation of the reverse search algorithm for vertex enumeration`http://cgm.cs.mcgill.ca/~avis/C/lrs.html`.**[MAGMA]**, ver. 2.13, by the Computational Algebra Group at the University of Sydney,`MAGMA`- high performance software for Algebra, Number Theory, and Geometry`http://magma.maths.usyd.edu.au/`.**[Polyhedral]**, by M. Dutour Sikirić,`Polyhedral`- a`GAP`package`http://www.liga.ens.fr/~dutour/Polyhedral/index.html`.

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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:
https://doi.org/10.1090/S0025-5718-2011-02528-7

Keywords:
Euclidean lattices,
quadratic forms,
linear codes

Received by editor(s):
April 20, 2009

Received by editor(s) in revised form:
January 29, 2011

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.