2011/05/13 by Bjoern Muetzel, Muetzel, Bjoern
Engineering · Mathematics · #11H56 #11H60 and 58D19 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.AG #msc:11H56 #msc:11H60 #msc:58D19
paper · pdf · doi:10.48550/arxiv.1105.2752
13 pages
openalex publication_date 2011/05/13 · arxiv created 2011/12/12 · arxiv updated 2011/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In section 1 we give an improved lower bound on Hermite's constant δ2g 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 2n are constructed with the help of a multiplicative matrix group isomorphic to (\Z2n,+). We furthermore show the connection of these lattices with the circulant matrices and the Barnes-Wall lattices.