author={Scott Duke Kominers},
  journal={International Journal of Number Theory},
  • S. Kominers
  • Published 21 June 2007
  • Mathematics
  • International Journal of Number Theory
We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. 
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L) + 2. This sharpens earlier results of Ozeki, and the second author and Abel,
Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)
Nous montrons que, si L est un reseau unimodulaire pair extremal de rang 40r avec r = 1,2,3, alors L est engendre par ses vecteurs de normes 4r et 4r + 2. Notre resultat est une extension de celui
Pseudo-normalized Hecke eigenform and its application to extremal $2$-modular lattices
It is shown that extremal $2-modular lattices of ranks $32$ and $48$ are generated by their vectors of minimal norm using the pseudo-normalized Hecke eigenform, the concept of which is introduced in this paper.
Configurations of Extremal Type II Codes via Harmonic Weight Enumerators
It is shown that for n ∈ {8, 24, 32, 48, 56, 72, 96} every extremal Type II code of length n is generated by its codewords of minimal weight.
Configurations of Extremal Type II Codes
Every extremal Type II code of length n is generated by its codewords of minimal weight, and "$t\frac12$-designs" is introduced as a discrete analog of Venkov's spherical designs of the same name.
Weighted Generating Functions and Configuration Results for Type II Lattices and Codes
We present an exposition of weighted theta functions, which are weighted generating functions for the norms and distribution of lattice vectors. We derive a decomposition theorem for the space of
Weighted Generating Functions for Type II Lattices and Codes
We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean


Even unimodular Euclidean lattices of dimension 32.II
The problem of generating 32-dimensional even unimodular Euclidean lattices by vectors of a given length is studied fully. It is proved that, apart from 15 exceptions, such lattices are generated by
Definite quadratische formen der dimension 24 und diskriminante 1
On even unimodular positive definite quadratic lattices of rank 32
Let Z be the ring of rational integers, and ~ the field of rational numbers. A finitely generated Z-module L in Q" with a positive definite metric is called a quadratic lattice. Since we treat only
Odd unimodular lattices of minimum 4
where n is the dimension of the lattice. The first case where this bound is not known to be tight is n = 72. It is much more difficult to obtain a good bound for the minimum of an odd unimodular
Lattices and Codes
This section introduces the basic concept of a lattice in ℝ n and describes the construction of lattices using LaSalle's inequality.
A Course in Arithmetic
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on
Sphere Packings, Lattices and Groups
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to
Sphere packing