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- W4297173291 abstract "In section 1 we give an improved lower bound on Hermite's constant $delta_{2g}$ for symplectic lattices in even dimensions ($g=2n$) by applying a mean-value argument from the geometry of numbers to a subset of symmetric lattices. Here we obtain only a slight improvement. However, we believe that the method applied has further potential. In section 2 we present new families of highly symmetric (symplectic) lattices, which occur in dimensions of powers of two. Here the lattices in dimension $2^n$ are constructed with the help of a multiplicative matrix group isomorphic to $({Z_2}^n,+)$. We furthermore show the connection of these lattices with the circulant matrices and the Barnes-Wall lattices." @default.
- W4297173291 created "2022-09-27" @default.
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- W4297173291 date "2011-05-13" @default.
- W4297173291 modified "2023-09-28" @default.
- W4297173291 title "A new lower bound for Hermite's constant for symplectic lattices" @default.
- W4297173291 doi "https://doi.org/10.48550/arxiv.1105.2752" @default.
- W4297173291 hasPublicationYear "2011" @default.
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