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Wir sind gerne für Sie daWe now apply the algorithm above to find the 121 orbits of norm -2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann -4 vectors from the vectors of nann 0 and -2. The neighbors of a strictly 24 dimensional odd unimodular lattice can be found as follows. If a norm -4 vector v E II. corresponds to the sum 25 1 of a strictly 24 dimensional odd unimodular lattice A and a !-dimensional lattice, then there are exactly two nonn-0 vectors of ll25,1 having inner product -2 with v, and these nann 0 vectors correspond to the two even neighbors of A. The enumeration of the odd 24-dimensional lattices. Figure 17.1 shows the neighborhood graph for the Niemeier lattices, which has a node for each Niemeier lattice. If A and B are neighboring Niemeier lattices, there are three integral lattices containing A n B, namely A, B, and an odd unimodular lattice C (cf. [Kne4]). An edge is drawn between nodes A and B in Fig. 17.1 for each strictly 24-dimensional unimodular lattice arising in this way. Thus there is a one-to-one correspondence between the strictly 24-dimensional odd unimodular lattices and the edges of our neighborhood graph. The 156 lattices are shown in Table 17.I. Figure I 7. I also shows the corresponding graphs for dimensions 8 and 16.
Produkteigenschaften
- Artikelnummer: 9780387985855
- Medium: Buch
- ISBN: 978-0-387-98585-5
- Verlag: Springer
- Erscheinungstermin: 07.12.1998
- Sprache(n): Englisch
- Auflage: 3rd Auflage 1999
- Serie: Grundlehren der mathematischen Wissenschaften
- Produktform: Gebunden
- Gewicht: 1326 g
- Seiten: 706
- Format (B x H x T): 160 x 241 x 48 mm
- Ausgabetyp: Kein, Unbekannt
Themen
- Interdisziplinäres
- Wissenschaften
- Wissenschaften: Forschung und Information
- Informationstheorie, Kodierungstheorie
- Mathematik | Informatik
- Mathematik
- Numerik und Wissenschaftliches Rechnen
- Angewandte Mathematik, Mathematische Modelle
- Interdisziplinäres
- Wissenschaften
- Wissenschaften: Forschung und Information
- Informationstheorie, Kodierungstheorie