Characteristic vectors of unimodular lattices which represent two
Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 405-414.

On améliore un majorant connu pour la dimension n d’un réseau unimodulaire indécomposable dont la longuer de l’ombre prend la troisième plus grande valeur possible, n-16.

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.

@article{JTNB_2007__19_2_405_0,
     author = {Mark Gaulter},
     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},
     zbl = {pre05302782},
     mrnumber = {2394894},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.594/}
}
Mark Gaulter. Characteristic vectors of unimodular lattices which represent two. Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 405-414. doi : 10.5802/jtnb.594. https://jtnb.centre-mersenne.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 1662447 | Zbl 0634.52002

[2] N. D. Elkies, A characterization of the n lattice. Math Res. Lett. 2 (1995), 321–326. | MR 1338791 | Zbl 0855.11032

[3] N. D. Elkies, Lattices and codes with long shadows. Math Res. Lett. 2 (1995), 643–651. | MR 1359968 | Zbl 0854.11021

[4] P. Gaborit, Bounds for certain s-extremal lattices and codes. Preprint. | Zbl 1127.11046

[5] M. Gaulter, Characteristic Vectors of Unimodular Lattices over the Integers. Ph.D. Thesis, University of California, Santa Barbara, 1998. | MR 1637828

[6] M. Gaulter, Lattices without short characteristic vectors. Math Res. Lett. 5 (1998), 353–362. | MR 1637828 | Zbl 0930.11045

[7] L. J. Gerstein, Characteristic elements of unimodular lattices. Linear and Multilinear Algebra 52 (2004), 381–383. | MR 2075038 | Zbl 1095.11021

[8] J. Martinet, Réseaux Euclidiens Designs Sphériques et Formes Modulaires. L’Enseignement Mathématique, Geneva, 2001. | Zbl 1054.11034

[9] G. Nebe and B. Venkov, Unimodular Lattices with Long Shadow. J. Number Theory 99 (2003), 307–317. | MR 1968455 | Zbl 1081.11049