Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.

Gabriele Nebe[1]; Elisabeth Nossek[1]; Boris Venkov[2]

  • [1] Lehrstuhl D für Mathematik RWTH Aachen University 52056 Aachen Germany
  • [2] Boris Venkov died in November 2011 before we could finish the paper

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 1, page 147-161
  • ISSN: 1246-7405

Abstract

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A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.

How to cite

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Nebe, Gabriele, Nossek, Elisabeth, and Venkov, Boris. "Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.." Journal de Théorie des Nombres de Bordeaux 25.1 (2013): 147-161. <http://eudml.org/doc/275758>.

@article{Nebe2013,
abstract = {A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.},
affiliation = {Lehrstuhl D für Mathematik RWTH Aachen University 52056 Aachen Germany; Lehrstuhl D für Mathematik RWTH Aachen University 52056 Aachen Germany; Boris Venkov died in November 2011 before we could finish the paper},
author = {Nebe, Gabriele, Nossek, Elisabeth, Venkov, Boris},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {extreme lattices; spherical designs; strongly perfect lattices; dual strongly perfect lattices},
language = {eng},
month = {4},
number = {1},
pages = {147-161},
publisher = {Société Arithmétique de Bordeaux},
title = {Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.},
url = {http://eudml.org/doc/275758},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Nebe, Gabriele
AU - Nossek, Elisabeth
AU - Venkov, Boris
TI - Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/4//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 1
SP - 147
EP - 161
AB - A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.
LA - eng
KW - extreme lattices; spherical designs; strongly perfect lattices; dual strongly perfect lattices
UR - http://eudml.org/doc/275758
ER -

References

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  2. K. M. Anstreicher, Improved linear programming bounds for antipodal spherical codes. Discrete Comput. Geom. 28 (2002), 107–114. Zbl1175.90284MR1904012
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  5. J. Martinet, Perfect lattices in euclidean space. Springer Grundlehren 327 (2003). Zbl1017.11031MR1957723
  6. G. Nebe, B. Venkov, The strongly perfect lattices of dimension 10. J. Théorie de Nombres de Bordeaux 12 (2000), 503–518. Zbl0997.11049MR1823200
  7. G. Nebe, B. Venkov, Low dimensional strongly perfect lattices I: The 12-dimensional case. L’enseignement Mathématique 51 (2005), 129–163. Zbl1124.11031MR2154624
  8. G. Nebe, B. Venkov, Low dimensional strongly perfect lattices III: The dual strongly perfect lattices of dimension 14. Int. J. Number Theory 6 (2010), 387–409. Zbl1219.11103MR2646763
  9. E. Nossek, On low dimensional strongly perfect lattices. PhD thesis, RWTH Aachen university, 2013. Zbl1271.11069
  10. B. Venkov, Réseaux et designs sphériques. Monogr. Ens. Math. 37 (2001), 10–86. Zbl1139.11320MR1878745

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