Geodesic
On integral lattices having an odd minimum
Algebra i analiz, Tome 16 (2004) no. 3, pp. 99-142.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the kissing number of integral lattices of odd minimum, with special emphasis on the case of minimum 3.
Keywords: euclidean lattices, kissing number. 
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J. Martinet; B. Venkov. On integral lattices having an odd minimum. Algebra i analiz, Tome 16 (2004) no. 3, pp. 99-142. http://geodesic.mathdoc.fr/item/AA_2004_16_3_a3/

[B-G] Bachoc C., Gaborit Ph., “Designs and self-dual codes with long shadows”, J. Combin. Theory Ser. A, 105 (2004), 15–34 | DOI | MR | Zbl

[Bt] Batut C., “Classification of quintic eutactic forms”, Math. Comp., 70 (2001), 395–417 | DOI | MR | Zbl

[Bt-M] Batut C., Martinet J., A catalogue of perfect lattices, http://www.math.u-bordeaux.fr/martinet

[Be] Bergé A.-M., “On certain Coxeter lattices without perfect sections”, J. Algebraic Combin., 20:1 (2004), 5–16 | DOI | MR | Zbl

[PARI] Cohen H. et al., User's guide to PARI, http://www.parigp-home.de

[C-E] Cohn H., Elkies N., “New upper bounds on sphere packings. I”, Ann. of Math. (2), 157 (2003), 689–714 | DOI | MR | Zbl

[C-S] Conway J. H., Sloane N. J. A., Sphere packings, lattices and groups, Grundlehren Math. Wiss., 290, Springer-Verlag, New York, 1988 ; 2nd ed., 1993; 3rd ed., 1999 | MR | Zbl

[C-Sl] Conway J. H., Sloane N. J. A., “Low-dimensional lattices. V. Integral coordinates for integral lattices”, Proc. Roy. Soc. London Ser. A, 426 (1989), 211–232 | DOI | MR | Zbl

[C-S2] Conway J. H., Sloane N. J. A., “On lattices equivalent to their duals”, J. Number Theory, 48 (1994), 373–382 | DOI | MR | Zbl

[J] Jaquet D.-O., Énumération complète des classes de formes parfaites en dimension 7, Thèse, Neuchâtel, 1991 | MR

[M] Martinet J., Perfect lattices in Euclidean spaces, Grundlehren Math. Wiss., 327, Springer-Verlag, Berlin, 2003, updated english version of “Les reseaux parfaits des espaces euclidiens”, Masson, Paris, 1996 | MR | Zbl

[M1] Martinet J., “Sur l'indice d'un sous-réseau with an appendix by C. Batut”, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., 37, Enseignement Math., Geneva, 2001, 163–211 | MR | Zbl

[N-V] Nebe G., Venkov B., “The strongly perfect lattices in dimension 10”, J. Théor. Nombres Bordeaux, 12 (2000), 503–518 | MR | Zbl

[Neu] Neumaier A., “On norm three vectors in integral Euclidean lattices. I”, Math. Z., 183 (1983), 565–574 | DOI | MR | Zbl

[Pl-P] Plesken W., Pohst M., “Constructing integral lattices with prescribed minimum. I”, Math. Comp., 45 (1985), 209–221, S5–S16 | DOI | MR | Zbl

[S-Y] Shult E., Yanushka A., “Near $n$-gons and line systems”, Geom. Dedicata, 9 (1980), 1–72 | DOI | MR | Zbl

[V] Venkov B. B., “Réseaux et designs sphériques”, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., 37, Enseignement Math., Geneva, 2001, 10–86 | MR | Zbl

[Wl] Watson G. L., “On the minimum points of a positive quadratic form”, Mathematika, 18 (1971), 60–70 | MR | Zbl

[W2] Watson G. L., “The number of minimum points of a positive quadratic form having no perfect binary section with the same minimum”, Proc. London Math. Soc. (3), 24 (1972), 625–646 | DOI | MR | Zbl