The lattices \(BW_{32}\) and \(U_{32}\) are equivalent. (Les réseaux \(BW_{32}\) et \(U_{32}\) sont équivalents.) (French) Zbl 0818.11027

The authors show that a certain 32-dimensional even unimodular lattice considered by J. Martinet is isometric to the well-known Barnes-Wall lattice of this dimension.


11H31 Lattice packing and covering (number-theoretic aspects)
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[1] Barnes, E.S. and Wall, G.E., Some extreme forms defined in terms of abelian groups, Journal of the Australian Mathematical Society, 1 (1959), 47-63. · Zbl 0109.03304
[2] Conway, J.H. and Pless, V., On the enumeration of self-dual codes, Journal of Combinatorial Theory Ser.A 28 (1980), 26-53. · Zbl 0439.94011
[3] Conway, J.H. and Sloane, N.J.A., Sphere packings, lattices and groups, Springer-Verlag, 2nd édition, 1992. · Zbl 0785.11036
[4] Coulangeon, R., Réseaux quaternioniens et invariant de Venkov, Manuscripta Mathematica82 (1994), 41-50. · Zbl 0797.11041
[5] Forney, G.D.Coset codes - part I, Introduction and geometrical classification, IEEE Trans. Inform. Theory, 34,5 (1988), 1123-1151. · Zbl 0665.94018
[6] Forney, G.D.Coset codes - part II, Binary lattices and related codes, IEEE Trans. Inform. Theory, 34,5 (1988), 1152-1187. · Zbl 0665.94019
[7] Martinet, J., Les réseaux parfaits des espaces euclidiens. En préparation. · Zbl 0869.11056
[8] Martinet, J., Structures algébriques sur les réseaux, Séminaire de théorie des nombres de Paris (1993). Cambridge University Press. A paraître. · Zbl 0829.11035
[9] Koch, H. und Venkov, B., Über ganzhalige unimodulare euklidische Gitter, J. reine angew. Math.398 (1989), 144-168. · Zbl 0667.10020
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