CONFIGURATIONS OF EXTREMAL EVEN UNIMODULAR LATTICES

@article{Kominers2009CONFIGURATIONSOE,
  title={CONFIGURATIONS OF EXTREMAL EVEN UNIMODULAR LATTICES},
  author={Scott Duke Kominers},
  journal={International Journal of Number Theory},
  year={2009},
  volume={05},
  pages={457-464}
}
  • 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. 
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7 Citations
Background Citations
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7 Citations

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
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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
TLDR
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
TLDR
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…

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