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\(BW_{32}\) Barnes-Wall lattice[1]

Description

BW lattice in dimension \(32\).

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The union of RM\((1,5)\) and 2RM\((3,5)\) codes yields a Type II self-dual linear code over \(\mathbb{Z}_4\) that then gives rise to the \(B_{32}\) Barnes-Wall lattice via Construction \(A_4\) [2,3].
\(BW_{32}\) Barnes-Wall lattice

References

[1]
E. S. Barnes and G. E. Wall, “Some extreme forms defined in terms of Abelian groups”, Journal of the Australian Mathematical Society 1, 47 (1959) DOI
[2]
P. Sole, "Generalized theta functions for lattice vector quantization", in Coding and Quantization, DIMACS Series in Dr,crete Mathenulies and Theoretical Computer Science, vol. 14. Providence, RH: American Math. Soc., 1993, pp. 27-32.
[3]
A. Bonnecaze, P. Sole, and A. R. Calderbank, “Quaternary quadratic residue codes and unimodular lattices”, IEEE Transactions on Information Theory 41, 366 (1995) DOI
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Zoo Code ID: bw32

Cite as:
\(BW_{32}\) Barnes-Wall lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bw32
BibTeX:
@incollection{eczoo_bw32, title={\(BW_{32}\) Barnes-Wall lattice}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bw32} }
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Permanent link:
https://errorcorrectionzoo.org/c/bw32

Cite as:

\(BW_{32}\) Barnes-Wall lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bw32

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/sphere_packing/lattice/bw/bw32.yml.