Characteristic vectors of unimodular lattices which represent two

Mark Gaulter[1]

  • [1] 446 Nineteenth Avenue Northeast Saint Petersburg, Florida 33704 États-Unis d’Amérique

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 2, page 405-414
  • ISSN: 1246-7405

Abstract

top
We improve the known upper bound of the dimension n of an indecomposable unimodular lattice whose shadow has the third largest possible length, n - 16 .

How to cite

top

Gaulter, Mark. "Characteristic vectors of unimodular lattices which represent two." Journal de Théorie des Nombres de Bordeaux 19.2 (2007): 405-414. <http://eudml.org/doc/249956>.

@article{Gaulter2007,
abstract = {We improve the known upper bound of the dimension $n$ of an indecomposable unimodular lattice whose shadow has the third largest possible length, $n-16$.},
affiliation = {446 Nineteenth Avenue Northeast Saint Petersburg, Florida 33704 États-Unis d’Amérique},
author = {Gaulter, Mark},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {2},
pages = {405-414},
publisher = {Université Bordeaux 1},
title = {Characteristic vectors of unimodular lattices which represent two},
url = {http://eudml.org/doc/249956},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Gaulter, Mark
TI - Characteristic vectors of unimodular lattices which represent two
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 2
SP - 405
EP - 414
AB - We improve the known upper bound of the dimension $n$ of an indecomposable unimodular lattice whose shadow has the third largest possible length, $n-16$.
LA - eng
UR - http://eudml.org/doc/249956
ER -

References

top
  1. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. Third Edition, Springer-Verlag New York, 1999. Zbl0634.52002MR1662447
  2. N. D. Elkies, A characterization of the ℤ n lattice. Math Res. Lett. 2 (1995), 321–326. Zbl0855.11032MR1338791
  3. N. D. Elkies, Lattices and codes with long shadows. Math Res. Lett. 2 (1995), 643–651. Zbl0854.11021MR1359968
  4. P. Gaborit, Bounds for certain s-extremal lattices and codes. Preprint. Zbl1127.11046
  5. M. Gaulter, Characteristic Vectors of Unimodular Lattices over the Integers. Ph.D. Thesis, University of California, Santa Barbara, 1998. Zbl0930.11045MR1637828
  6. M. Gaulter, Lattices without short characteristic vectors. Math Res. Lett. 5 (1998), 353–362. Zbl0930.11045MR1637828
  7. L. J. Gerstein, Characteristic elements of unimodular lattices. Linear and Multilinear Algebra 52 (2004), 381–383. Zbl1095.11021MR2075038
  8. J. Martinet, Réseaux Euclidiens Designs Sphériques et Formes Modulaires. L’Enseignement Mathématique, Geneva, 2001. Zbl1054.11034
  9. G. Nebe and B. Venkov, Unimodular Lattices with Long Shadow. J. Number Theory 99 (2003), 307–317. Zbl1081.11049MR1968455

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.