\(BW_{32}\) Barnes-Wall lattice[1]
Description
BW lattice in dimension \(32\).Cousins
- \(C_{m,r}\) code— The \(C_{m=5,r=1}\) code gives rise to the \(BW_{32}\) Barnes-Wall lattice via Construction \(A_4\) [2,3].
- \(BW_{32}\) lattice-shell code— The \(BW_{32}\) lattice-shell code is obtained from a shell of the \(BW_{32}\) Barnes-Wall lattice.
Member of code lists
Primary Hierarchy
Parents
The \(C_{m=5,r=1}\) code gives rise to the \(BW_{32}\) 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 Discrete Mathematics and Theoretical Computer Science, vol. 14. Providence, RH: American Mathematical Society, 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 (2026-06-08) — most recent
- Victor V. Albert (2022-11-22)
Cite as:
“\(BW_{32}\) Barnes-Wall lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bw32, arXiv:2606.11484