In this paper, we construct many new extremal Type II Z 6 -codes of length 24, and consequently we show that there is at least one extremal Type II Z 6 -code C of length 24 such that the binary and ternary reductions of C are B and T , respectively, for every binary Type II code B and every extremal
โฆ LIBER โฆ
Z4-Code Constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice
โ Scribed by Masaaki Harada; Masaaki Kitazume
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 121 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
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โฆ Synopsis
In this note, we give Z 4 -code constructions of the Niemeier lattices, showing their embedding in the Leech lattice. These yield an alternative proof of a recent result by Dong et al. [5].
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In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k ( 2) which is not of the form 11 r . In this paper, this problem is completely settled by finding such a basis f