Abstract
This paper is connected with the fundamental work of E.S. Barnes and G.E. Wall [1] in which the authors defined the so-called Barnes-Wall lattice. We shall determine the number of minima of some special sublattices of dimension 2n−k of this lattice, where 1≤k≤n.
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References
E. S. Barnes andG. E. Wall, Some extreme forms defined in terms of Abelian groups,Journal of the Australian Math. Soc. (1959), 47–63.
J. M. Conway andN. J. A. Sloane,Sphere Packings, Lattices and Groups, Springer-Verlag (1988).
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J. Leech, Some sphere packings in higher space.Canadian J. Math. 16 (1964).
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Supported by Hung. Nat. Found for Sci. Research (OTKA) grant no. 1615 (1992)
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Horváth, Á.G. On the sublattices of the Barnes-wall lattice. Period Math Hung 31, 131–138 (1995). https://doi.org/10.1007/BF01876488
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DOI: https://doi.org/10.1007/BF01876488