We improve the known upper bound of the dimension of an indecomposable unimodular lattice whose shadow has the third largest possible length, .
On améliore un majorant connu pour la dimension d’un réseau unimodulaire indécomposable dont la longuer de l’ombre prend la troisième plus grande valeur possible, .
@article{JTNB_2007__19_2_405_0, author = {Gaulter, Mark}, title = {Characteristic vectors of unimodular lattices which represent two}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {405--414}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {2}, year = {2007}, doi = {10.5802/jtnb.594}, mrnumber = {2394894}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.594/} }
TY - JOUR AU - Gaulter, Mark TI - Characteristic vectors of unimodular lattices which represent two JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 405 EP - 414 VL - 19 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.594/ DO - 10.5802/jtnb.594 LA - en ID - JTNB_2007__19_2_405_0 ER -
%0 Journal Article %A Gaulter, Mark %T Characteristic vectors of unimodular lattices which represent two %J Journal de théorie des nombres de Bordeaux %D 2007 %P 405-414 %V 19 %N 2 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.594/ %R 10.5802/jtnb.594 %G en %F JTNB_2007__19_2_405_0
Gaulter, Mark. Characteristic vectors of unimodular lattices which represent two. Journal de théorie des nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 405-414. doi : 10.5802/jtnb.594. http://archive.numdam.org/articles/10.5802/jtnb.594/
[1] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. Third Edition, Springer-Verlag New York, 1999. | MR | Zbl
[2] N. D. Elkies, A characterization of the lattice. Math Res. Lett. 2 (1995), 321–326. | MR | Zbl
[3] N. D. Elkies, Lattices and codes with long shadows. Math Res. Lett. 2 (1995), 643–651. | MR | Zbl
[4] P. Gaborit, Bounds for certain s-extremal lattices and codes. Preprint. | Zbl
[5] M. Gaulter, Characteristic Vectors of Unimodular Lattices over the Integers. Ph.D. Thesis, University of California, Santa Barbara, 1998. | MR
[6] M. Gaulter, Lattices without short characteristic vectors. Math Res. Lett. 5 (1998), 353–362. | MR | Zbl
[7] L. J. Gerstein, Characteristic elements of unimodular lattices. Linear and Multilinear Algebra 52 (2004), 381–383. | MR | Zbl
[8] J. Martinet, Réseaux Euclidiens Designs Sphériques et Formes Modulaires. L’Enseignement Mathématique, Geneva, 2001. | Zbl
[9] G. Nebe and B. Venkov, Unimodular Lattices with Long Shadow. J. Number Theory 99 (2003), 307–317. | MR | Zbl
Cited by Sources: