\(BW_{32}\) Barnes-Wall lattice[1]
Description
BW lattice in dimension \(32\).Cousins
- Reed-Muller (RM) code— 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].
- \(BW_{32}\) lattice-shell code
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Parents
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
Page edit log
- Victor V. Albert (2022-11-22) — most recent
Cite as:
“\(BW_{32}\) Barnes-Wall lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bw32