## Description

Lattice-based \(n\)-dimensional code whose codewords form the dual of the \(A_n\) lattice.

## Protection

Exhibits the thinnest covering in two dimensions and the thinnest lattice covering in dimensions three [1], four [2], and five [3,4].

## Parent

## Child

- Body-centered cubic (bcc) lattice code — The bcc lattice is the dual of the \(A_3=D_3\) fcc lattice.

## Cousin

## References

- [1]
- Bambah, R. P., and H. Gupta. "On lattice coverings by spheres." Proceedings of the National Institute of Sciences of India. Vol. 20. Indian National Science Academy, 1954.
- [2]
- Delaunay, B. N., and S. S. Ryskov. "Solution of the problem of least dense lattice covering of a four-dimensional space by equal spheres." Sov. Math. Dokl. Vol. 4. 1963.
- [3]
- S. S. Ryshkov, E. P. Baranovskii, “Solution of the problem of least dense lattice covering of five-dimensional space by equal spheres”, Dokl. Akad. Nauk SSSR, 222:1 (1975), 39–42
- [4]
- S. S. Ryshkov, E. P. Baranovskii, “C-types of n-dimensional lattices and 5-dimensional primitive parallelohedra (with application to the theory of coverings)”, Trudy Mat. Inst. Steklov., 137, 1976, 3–131; Proc. Steklov Inst. Math., 137 (1976), 1–140

## Page edit log

- Victor V. Albert (2022-02-26) — most recent

## Cite as:

“\(A_n^{\perp}\) lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/an_dual