منابع مشابه
A mass formula for unimodular lattices with no roots
We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada’s formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n ≤ 30. In particular, we find the mass of even unimodular 32dimensional lattices with...
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For each prime l with l ≡ 7 (mod 8), we define an action of the ring O = Z[ 2(1 + √ −l)] on the unimodular lattice D l+1 using a Paley matrix. We determine the isomorphism class of D l+1 as an O-module. In particular we show that unless l = 7, D l+1 is not a free O-module. We note a consequence for the Leech lattice.
متن کاملConference Matrices and Unimodular Lattices
We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...
متن کاملUniversal codes and unimodular lattices
Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4. We prove in a direct way the equivalence of these two constructions for p ~ 31. In dimension 32, we obtain an extremal lattice of type II not isometric...
متن کاملThe Unimodular Lattices of Dimension up to 23 and the Minkowski-Siegel Mass Constants
In an earlier paper we enumerated the integral lattices of determinant one and dimension not exceeding 20. The present paper extends this enumeration to dimension 23, finding 40 lattices of dimension 21, 68 of dimension 22, and 117 of dimension 23. We also give explicit formulae for the Minkowski-Siegel mass constants for unimodular lattices (apparently not stated correctly elsewhere in the lit...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.02.007