\(\Lambda_{16}\) Barnes-Wall lattice[1]
Description
BW lattice in dimension \(16\).Protection
Exhibits the densest known lattice packing in 16 dimensions.Cousins
- \(\Lambda_{24}\) Leech lattice— The \(\Lambda_{16}\) Barnes-Wall lattice can be obtained from the Leech lattice by restricting to the fixed-point 16-dimensional subspace of an involution [2; Ch. 4, pg. 131].
- \([2^m,m+1,2^{m-1}]\) First-order RM code— Applying Construction B to the first-order RM\((1,4)\) code yields the \(\Lambda_{16}\) Barnes-Wall lattice [2; Ch. 4, pg. 130][3; Exam. 10.7.2].
- \(q\)-ary repetition code— The \(\Lambda_{16}\) Barnes-Wall lattice can be obtained from the \([4,1,4]\) repetition code over \(\mathbb{F}_9\) via Quebbemann’s construction [2; Ch. 8, pg. 219].
- \(\Lambda_{16}\) lattice-shell code— The \(\Lambda_{16}\) lattice-shell code is obtained from a shell of the \(\Lambda_{16}\) lattice.
Member of code lists
Primary Hierarchy
Parents
\(\Lambda_{16}\) 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]
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
- [3]
- T. Ericson and V. A. Zinoviev, eds., Codes on Euclidean Spheres (Elsevier, 2001)
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2022-11-22)
Cite as:
“\(\Lambda_{16}\) Barnes-Wall lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lambda16, arXiv:2606.11484