Characteristic vectors of unimodular lattices which represent two

Gaulter, Mark

doi:10.5802/jtnb.594

Gaulter, Mark ¹

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

Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 405-414.

Résumé
Abstract

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, $n - 16$ .

DOI : 10.5802/jtnb.594

Affiliations des auteurs :

Gaulter, Mark ¹

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

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Gaulter, Mark. 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://www.numdam.org/articles/10.5802/jtnb.594/

Bibliographie
Cité par

[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 $ℤ^{n}$ 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

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Ernvall-Hytonen, Anne-Maria Some Results Related to the Conjecture by Belfiore and Solé, IEEE Transactions on Information Theory, Volume 60 (2014) no. 5, p. 2805 | DOI:10.1109/tit.2014.2311075
HARADA, MASAAKI CONSTRUCTION OF SOME UNIMODULAR LATTICES WITH LONG SHADOWS, International Journal of Number Theory, Volume 07 (2011) no. 05, p. 1345 | DOI:10.1142/s1793042111004794

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